SUPREM-IV.GS
Two Dimensional Process
Simulation for Silicon and
Gallium Arsenide
Edited by
S. E. Hansen and M. D. Deal
Integrated Circuits Laboratory
Stanford University
Stanford, California 94305
Copyright 1993
by The Board of Trustees of Leland Stanford
Junior University.
All rights reserved.
SUPREM, SUPREM-III, SUPREM-IV, and
PISCES, are registered trademarks of Stanford
University.
UNIX is a registered trademark of UNIX
Systems Labs, Inc.
Table of Contents
Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Adding SUPREM 3.5’s GaAs Models and Parameters to
SUPREM-IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
User’s Reference Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
The SUPREM-IV.GS Shell
DEFINE . . . . . . . .
FOR, FOREACH . . .
HELP . . . . . . . . .
MAN . . . . . . . . . .
SET . . . . . . . . . .
SOURCE. . . . . . . .
UNDEF . . . . . . . .
UNSET. . . . . . . . .
Commands . . . . . . . . .
BOUNDARY . . . . .
CONTOUR . . . . . .
CPULOG . . . . . . .
DEPOSIT . . . . . . .
DIFFUSE . . . . . . .
ECHO . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.23
.29
.31
.33
.34
.36
.38
.39
.40
.43
.48
.50
.52
.54
.57
.62
i
Table of Contents
ETCH . . . . . .
IMPLANT . . . .
INITIALIZE . . .
LABEL. . . . . .
LINE . . . . . . .
METHOD . . . .
MODE . . . . . .
OPTION . . . . .
PAUSE. . . . . .
PLOT.1D. . . . .
PLOT.2D. . . . .
PRINT.1D . . . .
PRINTF . . . . .
PROFILE . . . .
REGION . . . . .
SELECT . . . . .
STRESS . . . . .
STRUCTURE . .
Models . . . . . . . .
ANTIMONY. . .
ARSENIC . . . .
BERYLLIUM . .
BORON . . . . .
CARBON . . . .
GENERIC . . . .
GERMANIUM .
INTERSTITIAL .
MAGNESIUM. .
MATERIAL . . .
OXIDE . . . . . .
ii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. .64
. .67
. .71
. .74
. .76
. .79
. .87
. .88
. .89
. .90
. .94
. .98
. 101
. 103
. 105
. 107
. 111
. 113
. 119
. 121
. 126
. 132
. 138
. 144
. 149
. 155
. 160
. 170
. 176
. 180
Table of Contents
PHOSPHORUS
SELENIUM . .
iSILICON . . .
TIN. . . . . . .
TRAP . . . . .
VACANCY . .
ZINC . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. 188
. 194
. 199
. 205
. 210
. 213
. 221
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
EXAMPLE 1:
EXAMPLE 2:
EXAMPLE 3:
EXAMPLE 4:
EXAMPLE 5:
EXAMPLE 6:
EXAMPLE 7:
EXAMPLE 8:
EXAMPLE 9:
EXAMPLE 10:
EXAMPLE 11:
EXAMPLE 12:
EXAMPLE 13:
EXAMPLE 14:
EXAMPLE 15:
EXAMPLE 16:
EXAMPLE 17:
Boron Anneal – 1D . . . . . . . . . . . . . . . . . .
Boron OED – 1D . . . . . . . . . . . . . . . . . . .
OED Time . . . . . . . . . . . . . . . . . . . . . . .
Boron OED – 2D . . . . . . . . . . . . . . . . . . .
LDD Cross Section . . . . . . . . . . . . . . . . . .
One Dimensional Oxide Growth . . . . . . . . . . .
Fully Recessed Oxide Growth . . . . . . . . . . . . .
Shear Stress . . . . . . . . . . . . . . . . . . . . . .
Stress Dependent Oxidation . . . . . . . . . . . . . .
GaAs MESFET Gate Simulation – 1D . . . . . . . .
GaAs Simulation – 2D. . . . . . . . . . . . . . . . .
Dopant Activation Model Example . . . . . . . . . .
Implanted and Annealed Beryllium . . . . . . . . . .
Grown-in and Annealed Beryllium . . . . . . . . . .
Annealing An Implant From Measured (SIMS) Data .
Two.Dim Diffusion With File Input Interstitials . . .
Full.Coupled Diffusion . . . . . . . . . . . . . . . .
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. 229
. 237
. 243
. 249
. 257
. 267
. 271
. 277
. 281
. 287
. 291
. 295
. 299
. 301
. 303
. 305
. 309
iii
Table of Contents
iv
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Acknowledgments
This manual, like the SUPREM-IV.GS program itself, is the work of many
people. The original SUPREM-IV manual was primarily written by Mark
E. Law with contributions by Conor Rafferty, Goodwin Chin, and ChihChuan Lin. The modifications and additions needed for SUPREM-IV.GS
were done by Michael D. Deal and Stephen E. Hansen.
Section
Introduction
Adding SUPREM 3.5’s GaAs Models ...
User’s Reference Manual
Examples
Contributors
M. Deal, S. E. Hansen
M. Deal, S. E. Hansen
M. E. Law, C. S. Rafferty,
G. Chin, C. C. Lin,
S. E. Hansen
M. E. Law, C. S. Rafferty,
M. Deal, S. E. Hansen
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
v
Acknowledgments
vi
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Introduction
SUPREM-IV.GS is the first version of SUPREM-IV which models GaAs
and its dopants in addition to modeling silicon fabrication technology.
SUPREM-IV is an advanced 2D process simulator originally developed
for submicron silicon structures. It provides cross-sections of arbitrary device structures based on physical models for ion implantation, diffusion,
oxidation and annealing. It is designed to interface with other programs
that accurately simulate etching and deposition of thin films on the semiconductor surface, although it includes basic models for these processes as
well. The program structure is designed to handle moving boundaries that
commonly occur during oxidation or during deposition or etching of thin
films. SUPREM-IV can model stress gradients produced by overlaying
films. The implantation, diffusion annealing and oxidation models are
point defect based and are believed to be the most advanced models used
in any process simulation program. While the oxidation capability will not
be needed for simulating GaAs structures, all the other modules can be directly applied to compound materials.
In version 9305 of SUPREM-IV.GS, we started with version 9130 of
SUPREM-IV and incorporated most of SUPREM 3.5’s 1D GaAs models
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
1
Introduction
and parameters. This involved modifying SUPREM-IV so that it recognizes a new semiconductor material and new dopants, and allows for new expressions and parameters for the GaAs dopants in terms of the various
fabrication processes.
SUPREM 3.5 was developed to provide 1D concentration-depth profiles
through arbitrary cross-sections of GaAs devices for the specific processing conditions being simulated. SUPREM 3.5 is primarily designed for
modeling processes used to make simple ion implanted MESFET and
JFET structures in semi-insulating GaAs, with or without buried p-layers.
The main processes modeled are ion implantation (into bare GaAs or
through a silicon nitride or oxide cap) and the activation anneal (which includes dopant diffusion and activation). The dopants modeled are: Si, Se,
Ge, and Sn (the 4 common n-type dopants); and Be, Mg, Zn, and C (the 4
common p-type dopants). Also modeled is the diffusion of non-implanted
dopants, such as those incorporated during MBE or MOCVD GaAs
growth, which sometimes have different effective diffusion coefficients
than implanted dopants. Incorporating GaAs and SUPREM 3.5’s models
and parameters into SUPREM-IV is only the first step. The simulator must
be able to take into account effects such as implant damage, substrate stoichiometry, and defects, all of which are important in GaAs processing.
More advanced models and parameters must be developed to model such
things as time-dependent diffusion, uphill diffusion, and time-dependent
activation and other “anomalous” phenomena, most of which are believed
to be related to point defects and their interactions with dopants. In addition, 2D effects during implantation, diffusion, etc. must be modeled. It is
planned that a version of SUPREM-IV.GS that models many of these effects and phenomena be released in 1994.
Even without those advanced models, a version of SUPREM-IV with
GaAs and SUPREM 3.5’s 1D parameters will be very useful. For one, it
will allow one to use SUPREM-IV’s point defect and 2D capabilities to
help develop the more advanced models for GaAs. Secondly, there are
2
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Introduction
many cases where simple SUPREM 3.5 type models are quite adequate to
model the fabrication process and having 2D capability will be very useful.
The following briefly summarizes what has been added to SUPREM-IV to
make this version 9305 of SUPREM-IV.GS. GaAs and eight GaAs
dopants have been added to SUPREM-IV. The Pearson-IV implantation
parameters have been included. The electron or hole dependent diffusion
coefficients have been put in for these dopants. Other parameters for
GaAs, such as segregation coefficients, intrinsic carrier concentrations,
and defect energy levels, have also been added. In addition, compensation
mechanisms for dopant activation and different diffusivities for implanted
versus grown-in dopants have been added. (These two capabilities were
not in the silicon-only versions of SUPREM-IV and were added especially
for GaAs. However, they may be useful for silicon modeling as well.)
SUPREM-IV.GS can now simulate implantation, film deposition and etching, and dopant diffusion for GaAs, as well as all the silicon capabilities.
In the following sections, the addition of GaAs and its SUPREM 3.5 process models to SUPREM-IV is discussed in more detail.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
3
Introduction
4
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs
Models and Parameters to
SUPREM-IV
Adding a New Semiconductor
The first task was to add a new semiconductor material to SUPREM-IV,
namely GaAs. This was a non-trivial task as SUPREM-IV had been designed with the implicit assumption that only those materials used in silicon device processing would be used. Every file had to be carefully
examined for those places that dealt with material specification. The properties of GaAs, in particular the intrinsic carrier concentration as a function of temperature, had to be added. In SUPREM 3.5, we had used an
extended expression for this from Blakemore’s analysis [1], which included temperature dependencies of the bandgap, the effective density of states
at the conduction and valence bands, and the effective masses. In order to
fit this into the form used in SUPREM-IV
n
(i.e. n i = n i .o × T i.Pow × e− ( ni.E ⁄ ( kT) ) ), the values from the Blakemore
expression were fit to this kind of equation for the temperature range of
500˚C to 1000˚C. From this, we determined that n i .0 = 4.0×1016, n i.Pow =
1.5, and n i.E = 0.905.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
5
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
Adding New Dopants
The eight dopants in SUPREM 3.5 were added to SUPREM-IV. These are
the four n-type, Si, Se, Ge, and Sn, and the four p-type, Be, Mg, Zn, and C.
As with the addition of GaAs as a new material, the addition of new impurities required careful examination of each routine, but since the original
authors have had to add additional impurities this task was more straightforward. One consequence of its bias towards silicon processing was the
assumption that materials and impurities could be unambiguously specified on the same input statement. So as not to confuse Si the dopant in
GaAs with Si the semiconductor, the designation isilicon (for “impurity
silicon”) is used for the former in command line designations. In
SUPREM 3.5, we include an algorithm based on energy/mass scaling to
simulate the implantation of any element in the periodic table in GaAs. To
do this, all elements of the periodic table must be included in the impurity
or dopant set in SUPREM-IV. We may want to add this to SUPREM-IV
eventually, but in this first version it is not done.
GaAs Implantation Models and Parameters
SUPREM 3.5 models implantation by using Pearson IV distributions, just
as in SUPREM-IV. The four Pearson IV moments (projected range, straggle, skewness, and kurtosis) were experimentally determined for four
dopants in GaAs (Si, Se, Be, and Mg) as functions of energy. It was previously determined that theoretical calculations of the as-implanted profiles,
such as by TRIM (a monte-carlo technique) or BTE (a Boltzmann transport equation method) do not adequately model implantation of ions in
crystalline solids such as Si or GaAs. These calculations assume an amorphous substrate and hence do not predict the tails in the profiles due to ion
channeling, nor do they estimate the projected range adequately. Based on
the extensive experimentation and modeling of four of the dopants in
6
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
GaAs, tables of Pearson-IV moments versus implant energy were constructed. Then based on empirically determined mass/energy scaling relationships, tables for the other four dopants, as well as for all elements in
GaAs, were built. (These have been shown to very accurately model implantation in GaAs). SUPREM-IV also models implantation using Pearson-IV moment/energy tables. The tables for the eight dopants in GaAs
have been added to SUPREM-IV’s implantation data files. In addition, the
experimentally determined Gaussian parameters for implanting dopants in
or through capping material (silicon nitride and oxide) have been copied
from SUPREM 3.5 into SUPREM-IV.
SUPREM-IV also includes a fifth moment, the lateral straggle, in order to
model the implantation profile in two dimensions. This moment was not
determined for SUPREM 3.5, but in order to put some first-order numbers
in for GaAs dopants, an algorithm based on TRIM results was developed.
Even though TRIM does not predict the absolute values very well for
GaAs, it does adequately predict trends and relationships. From tables of
Pearson IV moments produced by TRIM for the dopants in GaAs, it is
seen that ratio of the lateral straggle to normal straggle is fairly constant
with implant energy for each ion, and that this ratio scales with the log of
the ion mass. Assuming that this ratio is valid (as opposed to the actual
values of the moments), we calculated this ratio for each ion and applied it
to the experimentally determined normal straggles. From this, we determined that for each energy and dopant, the ratio of the lateral straggle (the
fifth Pearson IV moment) to the normal straggle (the second Pearson IV
moment) equals 1.83 - 0.525log(ion mass). The lateral straggles for each
dopant and energy were thus calculated and added to SUPREM-IV for the
eight dopants in GaAs.
SUPREM 3.5 includes implant profile dependencies on dose and cap type
and thickness. In general, we had experimentally determined that the tails
decreased: (1) as the implant dose increased and (2) when the implants
were done through oxide or nitride caps (in addition to changing the pro-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
7
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
jected range). Both these phenomena are presumably due to decreasing the
ion channeling, either by randomizing the ion trajectory or by decreasing
the channels. This is modeled in SUPREM 3.5 by adding an algorithm
which modifies the second Pearson-IV moment as a function of dose or
cap. SUPREM 3.5 is able to do this because the complete processing history is part of the structure information file. There is no capability for this
in SUPREM-IV, and will have to be added later.
SUPREM-IV.GS now allows one to specify the implant angle. Experimental determination of implant parameters for GaAs showed that the channeling was minimized for implant angles of greater than or equal to 10˚ to
the normal, and the default parameters correspond to that condition. For
now, specifying and angle of less than 10˚ will not increase the channeling
in the simulations (that will be added later), but “shadowing” is now simulated for non-zero degree implants.
GaAs Diffusion Models and Parameters
SUPREM-IV models dopant diffusion according to the following equation:
∂C A
∂t
= ∇ Dv CA
CV
*
CV
CV n
CI
CI n
∇ CA *  + DI CA * ∇ CA * 
 CV ni 
CI  CI ni 
(EQ 1)
where C is concentration, D is diffusivity, V is vacancy, I is interstitial, and
the “star” denotes equilibrium values. For p-type dopants, the electron
concentration, n, is replaced by the hole concentration, p. It is assumed
that the diffusion occurs via interstitials or vacancies, or a combination of
both. The full expressions for DV and DI, which are dependent on the fermi-level and on the fraction of interstitial-assisted diffusion (Fi ), as compared to that which diffuses via vacancies, are given in Table 1. We have
8
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
TABLE 1
Equation used in SUPREM-IV to model diffusion, based on interstitial and/or
vacancy mechanisms. Also given is the expression for a generic dopant used in
GaAs.
The diffusion equation solved by SUPREM-IV
∂C A
∂t
= ∇
Dv CA
CV
*
CV
CV n
CI
CI n
 +D C

∇  CA
∇  CA
I A *
*
*
n


C i
C
C ni 
V
for n-type dopants. For p-type dopants, replace the
I
I
n
p
by .
ni
ni
Generic Dopant:
DI = Fi ×
n
p
n 2
p 2
D x + D m   + D p   + D MM   + D PP  
 ni 
 ni 
 ni 
 ni 
DV = ( 1 − Fi ) ×
n 3
p 3
+ D MMM   + D PPP  
 ni 
 ni 
n
p
n 2
p 2
D x + D m   + D p   + D MM   + D PP  
n
n
n
n
 i
 i
 i
 i
n 3
p 3
+ D MMM   + D PPP  
 ni 
 ni 
Where Fi = fraction of Interstitialcy or interstitial-assisted diffusion and
(1-Fi ) = fraction of vacancy assisted diffusion.
Each
 − D XX. E 
D XX = D XX.0 exp
 kT 
previously determined that the four n-type dopants in GaAs diffuse via a
Ga vacancy mechanism ( F i = 0 ) and that the p-type dopants diffuse via a
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
9
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
Ga interstitial mechanism ( F i = 1 ) [1-4]. We have also shown that the
kick-out (or substitutional-interstitial diffusion mechanism), traditionally
used to model p-type diffusion in GaAs, results in virtually identical governing diffusion equations as used for interstitial diffusers in SUPREM-IV
for Si [4]. We have demonstrated that SUPREM-IV’s equation can be used
to successfully model the anomalous diffusion behavior of Mg in GaAs
when excess defects produced by implant damage are included. For these
reasons, it has been a relatively simple task to incorporate SUPREM 3.5’s
simple non-defect models and parameters into the SUPREM-IV framework. Basically, the expressions in SUPREM 3.5 were made to be the Di
and Dv terms for p-type dopants and n-type dopants, respectively [See the
1990 and 1992 Stanford Technical Reports, “Process Simulators for Silicon VLSI and High Speed GaAs Devices,” by Plummer, et al. for more
discussion on these values]. Two simple modifications to SUPREM 3.5’s
expressions were made. One was to include a ni term in the expressions for
the p-type dopants to fit the SUPREM-IV framework. In SUPREM 3.5,
the diffusivity expressions were derived based on the kick-out methodology and were not normalized to the intrinsic carrier concentration. This
modification involved changing the pre-exponential term and the exponential term (since ni is a function of temperature) of the diffusivities. The
other modification was due to the fact that the original n-type diffusivities
were derived without an electric field effect. Since an electric field effect is
built into SUPREM-IV’s diffusion equation, the numbers had to be re-derived, since the effect can increase the total diffusion by up to a factor of
two. All eight dopants were tested in SUPREM-IV (without any excess interstitials or vacancies) to ensure that their diffusion behavior for inert
conditions is the same as SUPREM 3.5 predicts.
SUPREM 3.5 has two sets of diffusivities for Mg in GaAs, one for temperatures below 825˚C and one for temperatures above 825˚C. For now we
use only the higher temperature values. Also, the diffusivity for grown-in
Zn has been modified due to recent re-analysis of the literature data.
10
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
The equations and parameters for the eight dopants in regards to diffusion
in GaAs are shown in Table 2 for the n-type dopants and in Table 3 for the
p-type dopants.
SUPREM 3.5 had two sets of diffusivities for dopants in GaAs: one for
dopants that were implanted, and one for dopants that were incorporated
during growth, or “grown-in.” For p-type dopants, the implanted values
are generally higher than the grown-in; for n-types the implanted values
are generally lower than the grown-in. These differences are believed to be
due to different point defect conditions caused by the introduction of the
dopants and the subsequent diffusion. For this first version of
SUPREM-IV.GS, we have used the SUPREM 3.5 convention of using different values of D for the two cases (in the future, physically correct models which take into account the different point defect conditions will be
used). SUPREM-IV.GS keeps track if a given dopant has been implanted
or not, and uses the appropriate value. (It assumes that if the dopant is not
implanted, it is grown-in. Gas source diffusions would therefore use the
grown-in values). If you want to use the implanted value for cases where
the dopant is not implanted in the input file (e.g. when a solid-source diffusion is done, or when a SIMS file is used as the initial dopant profile), then
one should do a very low dose implant (i.e. below the background level) of
that dopant so the program thinks that all of it has been implanted.
The SUPREM 3.5 default numbers for dopant diffusivity in cap material
(silicon oxide or nitride) used in GaAs technology have been added to
SUPREM-IV, as have the segregation and transport values across interfaces. Rather arbitrary default numbers for interstitial and vacancy diffusivity,
segregation, and transport parameters have also been added. These will be
updated when more reliable numbers are determined.
We have also added a generic dopant to SUPREM-IV.GS, whose diffusivity expression is shown in Table 1. This includes many n and p terms in
the expression and can be used to test other dopants and diffusivities for
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
11
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
TABLE 2
Expressions for diffusivities of n-type dopants in GaAs used in SUPREM-IV.GS.
IMPLANTED
Silicon (Si)
GROWN-IN
DV = ( 1 − Fi ) DX
n
D V = ( 1 − F i ) D MM  
 ni 
DI = Fi DX
Fi = 0
−9
D X.0 = 1.8 ×10
2
cm sec
−1
n
D I = F i D MM  
n
 
2
2
i
Fi = 0
D X.E = 1.6eV
2
D MM.0 = 33cm sec
−1
D MM.E = 3.9eV
Selenium (Se)
DV = ( 1 − Fi ) DX
n
D V = ( 1 − F i ) D MM  
n
 i
DI = Fi DX
Fi = 0
−8
D X.0 = 1.8 ×10
2
cm sec
−1
n
D I = F i D MM  
n
 
2
i
Fi = 0
D X.E = 1.6eV
2
D MM.0 = 1.2cm sec
D MM.E = 3.6eV
Tin (Sn)
n
D V = ( 1 − F i ) D MM  
n
 i
n
D I = F i D MM  
n
 
same as implanted
2
2
i
Fi = 0
1
2
D MM.0 = 9.6 ×10 cm sec
−1
D MM.E = 3.9eV
Germanium
(Ge)
n
D V = ( 1 − F i ) D MM  
 ni 
n
D I = F i D MM  
n 
same as implanted
2
2
i
Fi = 0
D MM.0 = 1.1 ×10
−3
2
cm sec
−1
D MM.E = 2.9eV
12
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
−1
2
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
TABLE 3
Expressions for diffusivities of p-type dopants in GaAs used in SUPREM-IV.GS
Beryllium
(Be)
IMPLANTED
GROWN-IN
p
DV = ( 1 − Fi ) DP  
 ni 
p
DI = Fi DP  
 ni 
p
DV = ( 1 − Fi ) DP  
 ni 
p
DI = Fi DP  
 ni 
Fi = 1
Fi = 1
−6
D P.0 = 2.1 ×10
2
cm sec
−1
D X.E = 1.74eV
Magnesium
(Mg)
p
DV = ( 1 − Fi ) DP  
 ni 
p
DI = Fi DP  
 ni 
2
cm sec
−1
p
DV = ( 1 − Fi ) DP  
 ni 
p
DI = Fi DP  
 ni 
Fi = 1
−2
D P.0 = 6.1 ×10
2
cm sec
−1
D P.E = 2.8eV
−3
D P.0 = 6.8 ×10
2
cm sec
−1
D P.E = 2.8eV
p
D V = ( 1 − F i ) D PP  
 ni 
p
D I = F i D PP  
 ni 
2
p
D V = ( 1 − F i ) D PP  
 ni 
2
p
D I = F i D PP  
 ni 
Fi = 1
2
2
Fi = 1
2
2
D PP.0 = 1.2 ×10 cm sec
Carbon (C)
−8
D PP.E = 1.74eV
Fi = 1
Zinc (Zn)
D PP.0 = 2.1 ×10
−1
1
D PP.0 = 15.6cm sec
D PP.E = 3.9eV
D PP.E = 3.9eV
DV = ( 1 − Fi ) DX
same as implanted
−1
DI = Fi DX
Fi = 1
− 16
D X.0 = 1.0 ×10
2
cm sec
−1
D X.E = 0.0eV
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
13
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
subsequent model development. (The default type of the generic dopant is
an acceptor.)
Since some dopants in GaAs are amphoteric and can be either donors or
acceptors under certain conditions, we have added the capability of changing the type of the impurity from its default to either donor or acceptor.
This is an impurity specification option.
GaAs Solubility and Activation Models
In SUPREM-IV one can specify the solubility of a dopant in a semiconductor as a function of temperature. Above that concentration, the dopant
is electrically inactive and immobile (the diffusivity is effectively zero).
Below that concentration, the dopant is electrically active and mobile. In
GaAs, for relatively low concentration levels of n-type dopants, not all the
dopants appear to be electrically active, yet they are all mobile. One way
to model this is to assume that below the solubility level, some dopants
may be inactive but all are mobile. A better way of explaining this, as is
done by Walukiewicz [5] and others recently, is that all or most are mobile
and electrically active, but there is some compensation mechanism (due to
the production of negatively charged Ga vacancies, for example) which reduces the net donor concentration. In SUPREM 3.5 the first method was
used, and empirical formulae were determined which calculated the active
fraction of each n-type dopant as a function of concentration and temperature. (Arsenic clustering in silicon was modeled in a somewhat similar
manner in SUPREM-IV.)
We have decided to model dopant activation for GaAs in SUPREM-IV using the second method. This is believed to be the more physically correct
model for the phenomena and will result in the compensation ratio, or
fraction inactive, to be based on the total doping, which is what is actually
14
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
observed, and not on each dopant individually, which is what is done in
SUPREM 3.5.
Until a defect-based compensation model is incorporated into
SUPREM-IV, a semi-empirical model will be used. The original algorithm in SUPREM 3.5, in addition to having the shortcomings mentioned
above, was based on limited data in the literature and resulted in errors at
high concentrations and temperatures. An expression for the compensation
effect has been determined by fitting recent modeling results of Vanasupa
[6] with an analytical equation, which is a function of net doping concentration, ( N D − N A ) , and temperature. (Vanasupa’s numbers are based
upon both experimental data and a specific compensation mechanism,
compensation by amphoteric pairs in her case, but the numbers would apply to any compensation mechanism.) The equation is:
( N D − N A ) effective =
( 2.20 − 0.00117T ) ( N D − N A )
18
1 + ( N D − N A ) ⁄ ( 1.25 ×10 )
(EQ 2)
where T is in degrees Kelvin. The compensation factor will be applied to
the net doping concentration calculation to get an effective net doping
concentration.
The expression for compensation is based on the equilibrium activation
numbers of Vanasupa [6]. She also determined that there is a time dependent, kinetic part to the activation process, important for short time activation anneals. This will also have to be included in future models for dopant
activation in GaAs.
The solubility values for dopants in GaAs are not well known. Until good
numbers are obtained, default values of 1×1019 cm3 will be used for all
dopants.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
15
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
GaAs Defect Parameters
SUPREM 3.5 does not consider point defects in its implantation, diffusion, or activation models. As discussed above, one of the prime motives
for incorporating GaAs into SUPREM-IV is to make use of
SUPREM-IV’s point defect capabilities, especially in regards to the effect
of point defects on dopant diffusion and activation. For the initial version
of SUPREM-IV for GaAs, we want to include some default numbers for
the defect parameters so we can start our development of future point-defect based models for diffusion and activation.
SUPREM-IV only considers one type of interstitial and one type of vacancy. In GaAs there are two types of each: Ga and As. Eventually we will
have to add both types to SUPREM-IV, but for now we will only assume
one type. (We have shown that for modeling diffusion of both n-type and
p-type dopants in GaAs, it is not a bad assumption to consider only the Ga
sublattice (see reference [4] for example), so this limitation may not
hinder us too much.)
The total number of defects and the distribution of each charge type is calculated by SUPREM-IV as a function of temperature and fermi-level. Using the energy levels of the variously charged vacancies and interstitials
calculated by Baraff and Schluter [7] and by Jansen et al. [8], the relative
probability of each charge state was calculated using the Shockley-Last
equations [9]. These numbers are given in Table 4. Since triply charged interstitials and vacancies are important in GaAs, and SUPREM-IV previously only included neutral through doubly charged defects, new
parameters had to be added.
Rather arbitrary default numbers for defect recombination (both surface
recombination and bulk I/V recombination) have been put in for Ga interstitials and vacancies
16
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
.
TABLE 4
Parameter values for Ga defect distributions used in SUPREM-IV
2
3
2
n
p
n
n
p
p
neu + neg   + dneg   + tneg   + pos   + dpos   + tpos  
ni 
ni 
ni 
ni 
ni 
ni 






*
C I = C star
neu + neg + dneg + tneg + pos + dpos + tpos
3
neu = neu.0 × exp ( neu.E ⁄ ( kT ) )
Gallium vacancies:
Gallium interstitials:
neu.0
neg.0
pos.0
dneg.0
dpos.0
tneg.0
tpos.0
= 1.0
= 0.0
= 0.053
= 0.0
= 0.0
= 0.0
= 0.0
neu.E
neg.E
pos.E
dneg.E
dpos.E
tneg.E
tpos.E
=
=
=
=
=
=
=
0.0
0.0
-0.788
0.0
0.0
0.0
0.0
neu.0
neg.0
pos.0
dneg.0
dpos.0
tneg.0
tpos.0
=
=
=
=
=
=
=
1.0
0.05305
0.0
0.00281
0.0
1.489×10-4
0.0
neu.E
neg.E
pos.E
dneg.E
dpos.E
tneg.E
tpos.E
=
=
=
=
=
=
=
0.0
-0.588
0.0
-0.856
0.0
-0.899
0.0
References
1. J.S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band
gap and effective mass parameters and derived independently from Cr
acceptor capture and emission coefficients,” J. Appl. Phys, 53, 520
(1982).
2. M.D. Deal, S.E. Hansen, and T.W. Sigmon, “SUPREM 3.5 - Process
Modeling of GaAs Integrated Circuit Technology,” IEEE Trans. CAD.,
9, 939 (1989).
3. K.H. Lee, D.A. Stevenson, and M.D. Deal, “Diffusion Kinetics of Si in
GaAs and Related Defect Chemistry,” J. Appl. Phys., 68, 4008 (1990).
4. H.G. Robinson, M.D. Deal, P.B. Griffin. G. Amaratunga, D.A. Steven-
son, and J.D. Plummer, “Modeling Uphill Diffusion of Mg Implants in
GaAs Using SUPREM-IV,” J. Appl. Phys., 71, 2615 (1992).
5. W. Walukiewicz, “Electron Scattering By Native Defects in Uniformly
and Modulation Doped Semiconductor Structures,” Mat. Res. Soc.
Proc., 163, 845 (1990).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
17
Adding SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV
6. L.S. Vanasupa, M.D. Deal, and J.D. Plummer, “Modeling Activation of
Implanted Si in GaAs,” J. Electrochem. Soc., 138, 2134 (1991).
7. G.A. Baraff and M. Schluter, “Electronic Structure, Total Energies, and
Abundances of the Elementary Point Defects in GaAs,” Phys. Rev.
Lett., 55, 1327 (1985).
8. R.W. Jansen, D.S. Wolde-Kidane, and O.F. Sankey, “Energetics and
Deep Levels of Interstitial Defects in the Compound Semiconductors
GaAs, AlAs, ZnSe, and ZnTe,” J. Appl. Phys., 64, 2415 (1988).
9. W. Shockley and J.T. Last, “Statistics of the Charge Distribution for a
Localized Flaw in a Semiconductor,” Phys. Rev., 107, 392 (1957).
18
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
User’s Reference Manual
INTRODUCTION
This manual describes SUPREM-IV.GS, a version of the process simulator SUPREM-IV extended to both GaAs and Silicon process simulation.
This manual is not intended as a tutorial guide on how to use
SUPREM-IV.GS, instead it is more of a reference to the commands and
capabilities. The manual is divided into four sections. The first section
(this section) provides an introduction and describes the conventions used
in the rest of the manual. Next is a section describing the commands that
are part of the interactive shell. The third section describes the commands
of SUPREM-IV.GS that perform actions. The final section documents the
model commands, most of which are used to set parameters. In that section the physics associated with SUPREM-IV.GS models is described and
referenced. Following the manual sections are a series of SUPREM-IV.GS
examples, which can be used to learn the program. The example input
decks are provided on the source code tape. A new user may want to start
in that section.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
19
User’s Reference Manual
CONVENTIONS
This section describes the use of the manual and the conventions used to
denote the parameters and choices associated with each statement. The
program accepts input in a fashion similar to SUPREM-III and PISCES-II.
The input is made up of a series of statements. It is important to bear in
mind that the parser is case sensitive, i.e. FOO is not the same as foo.
Each statement can have parameters which are of the form:
parameter_name = value
Value is either a real number expression or a character string. There are
some parameters that are booleans, which recognize true and false as special strings. If the value is left off a boolean parameter, it is set to true.
The manual describes these parameters in the following form:
param = <n>
a numerical valued parameter
param = <string>
a string valued parameter
param
a boolean parameter
Choices are denoted by putting the parameters in parenthesis and separating them by vertical bars. For example, ( par1 | par2 ) states that either
par1 or par2 may be specified but not both. Anything enclosed in brackets
[ ] are optional parameters and aren't necessary. Almost everything in the
program has some sort of default value, so almost all parameters are optional. In case of doubt, never rely on the defaults.
20
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
User’s Reference Manual
Floating point parameters can be specified as expressions involving numbers, numerical constants, the operators +, -, *, /, ^, and the functions listed
below.
abs
absolute value
active
active portion of the specified dopant
erf
error function
erfc
complimentary error function
exp
exponential
gradx
computes the rough gradient in the x direction
grady
computes the rough gradient in the y direction
log
logarithm
log10
logarithm base 10
mat1@mat2
returns the y value of the interface between mat1 &
and mat2 along a vertical slice at the given location.
scale
scales the value given by the maximum value
sqrt
square root
xfn
takes y and z and finds an x to match
yfn
takes x and z and finds an y to match
zfn
takes x and y and finds an z to match
If an expression contains spaces, it should be enclosed in parenthesis.
EXAMPLES
Par1=<n>
Par1 is a required numeric valued option.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
21
User’s Reference Manual
Par1=( 4.0 * exp( -2.0 / (8.62e-5 * 1173.0) ) )
Par1 is a required numeric valued option, assigned a real number expres-
sion.
[ Par2=<string> ]
Par2 is an optional character string variable.
SEE ALSO
select for how to choose a z variable, printf for further examples of ex-
pressions.
22
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
The SUPREM-IV.GS
Shell
DESCRIPTION
The shell is the user interface to the program. The shell was designed to be
similar to Unix’s® csh(1) shell and allow some of the same actions. The
shell is a command line interpreter. It reads commands from the user and
executes the commands with the arguments listed.
The shell executes commands from the system wide model file to set up
coefficients. It then executes commands from the file .supremrc before
providing a user prompt. This allows start up commands to be executed
before the session begins. The .supremrc file is looked for in the current
directory and the user's home directory.
COMMANDS
A simple command is a sequence of words, the first of which specifies the
command to be executed. Sequences of commands may be separated by
semicolons (;), and are then executed sequentially. A command may be
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
23
The SUPREM-IV.GS Shell
executed in background mode by following the last entry with an ampersand (&) character.
Any sequence may be placed in braces to form a simple command.
Built-In Command Summary
Built-in commands are executed within the shell. The built-in commands
are:
define
define name wordlist
define name( args ) wordlist
The first form prints all aliases. The second and third forms assign the
specified wordlist as the macro of name. Every occurrence of name in the
input stream is replaced by the wordlist associated with it. Optionally, as
shown in the third form, a definition can contain arguments which will be
mapped when the macro is substituted. name will only be substituted for
when it is separated by blank space or shell special characters.
foreach name ( val1, val2, val3 ) commands end
name is set to each of the values contained in the parenthesis consecutive-
ly and the commands are executed. This allows a command to be run several times with different parameters. name is substituted in the commands
using the macro features.
help command
help without any arguments will list all of the available commands. The
command “help command_name” will give information on the listed command name. When used in the second style, the help command provides a
list of parameters and short description of each of the parameters.
24
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
The SUPREM-IV.GS Shell
set ( echo | noexecute | prompt string )
This command allows the parameters listed to be changed. echo causes
the command buffer to be echoed. noexecute is described in the nonbuilt-in command section below. prompt is the string which appears when
the shell is ready to accept input. set with no input lists the current settings.
source filename
The source command allows the file filename to be opened and the contents of the file are placed in the input stream of the shell to be parsed.
undef name
This command removes the macro name from the macro table.
unset ( echo | noexecute )
This command turns off the echo or noexecute modes.
Non-Built-In Command Execution
If a command is entered that is not a built-in, the program checks its parse
tables for that command. If the command is found, that parameters are
passed to the command for execution.
If the noexecute flag is set, the command will only check on the parameters to see if they are legal. It will exit without performing any action other
that the check. This mode is useful for debugging long scripts of input.
Macro Substitution
A command line is scanned, it is parsed into distinct words and each word
is checked to see if it is in the macro table. If it is, then the text which is the
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
25
The SUPREM-IV.GS Shell
macro for that command is placed in the input stream. To disable macro
substitution, the % character can be used at the beginning of the line. That
line will not be macro expanded. Selective macro evaluation can be
achieved by disabling macros (with %) and putting $ before the names
which are desired to be evaluated. That is, use $name (or ${name} in cases of ambiguity). The intent is to provide shell variables in a simple way.
If a macro is found, substitution is performed of the macro body for the
macro name. Any arguments are paired up and they are substituted as
well. Macro arguments may not be other macros.
Command Line Parsing
The shell splits input lines into words at blanks and tabs. The following
exceptions (parser metacharacters) are considered separate words:
&
ampersand;
;
semicolon;
>
greater-than sign;
{
left brace;
}
right brace;
%
percent sign.
These characters have special meaning to the shell and are described elsewhere.
Input/Output
The standard output of a command may be redirected with the following
syntax: > name. The file is used as standard output. If the file does not exist then it is created; if the file exists, it is appended to. The entire output of
26
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
The SUPREM-IV.GS Shell
the sequence redirected is sent to the file. There is a limit on the number of
open files. It is not suggested that redirection be nested in a loop.
Background
Any sequence of commands may be backgrounded by using the & character. These commands will be executed using a fork and exec call. They
will work on the current state of the data space but will not modify the
copy you have. The copy will begin execution immediately and return a
prompt to the user without waiting for the copy to finish.
EXAMPLES
foo
execute command foo with no parameters.
foo val=1.0 file=name
execute command foo with parameter string val=1.0 file=name.
foo; bar
execute command foo followed by command bar
foo > name
execute command foo and sends it output into file name.
foo; bar > name
execute commands foo and bar and send their output to file name.
foo &
execute command foo in the background.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
27
The SUPREM-IV.GS Shell
BUGS
Numeric expressions are handled by an ad hoc parser, separate and different from the shell yacc parser. If a complicated expression gives unexpected results, parenthesize.
28
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
DEFINE
COMMAND
DEFINE
Define strings for command line substitution.
SYNOPSIS
define [ macro_name macro_body ]
DESCRIPTION
The define command can be used for command line substitution. The
name macro_name will be entered into a table with the macro_body. Any
time the macro_name appears on a command line as a separate token, the
macro_body is substituted. The macro_name can also appear following a
'$' which will force a macro substitution. To concatenate a macro with another string, $macro_name should be used. This allows long, often-used
sequences to be entered by the user once. It is similar to csh aliasing, except that it takes place anywhere on a command line.
define without any arguments will list the current definitions. To undefine
a name, use the undef command. If the user desires to turn off all macros
in a line, the % character can be used. A % will turn off macro expansion
from the % character to the end of a line.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
29
DEFINE
EXAMPLES
%define bounds xmin=0.0 xmax=5.0 ymin=0.0 ymax=20.0
This define will substitute all future occurrences of the string bounds with
the list of mins and maxs.
%define q quit
This will allow the user to exit SUPREM with a q instead of typing the quit
command.
echo $q $q q
If q has been defined as a macro equal to quit, all three instance will be expanded, and the output will look like:
quit quit quit
BUGS
The expansion routine does not recursively expand macros. It finds a token, and expands it once and then moves on. For example,
%define foo bar
%define froboz foo
froboz
will expand froboz to foo and no further.
SEE ALSO
The undef command.
30
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
FOR, FOREACH
COMMAND
FOR, FOREACH
Command looping facility.
SYNOPSIS
[ foreach | for ] name ( list )
commands
end
DESCRIPTION
The for command allows the user to specify loops in the input. Either for
or foreach is acceptable. name will take on the values in the list consecutively until the there are no values left. The body will be executed once for
each value in the list. Values in the list can be separated by commas or
spaces. name is set to the value in the list using the define feature of the
shell. Replacement of name in the body of the commands is done using
the macro features that are part of the normal shell.
The list is a set of strings separated by commas or spaces. It can also be
one of the following numerical operators:
start to end step val
where start is a numerical start value, end is the last value, and val is the
size of step to take between them.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
31
FOR, FOREACH
EXAMPLES
foreach string ( hello, goodbye, aufwiedersehn, goodnight )
echo string
end
The command “echo string” will be executed four times. string will be set
to the values “hello”, “goodbye”, “aufwiedersehn”, and “goodnight” consecutively. This will produce output that will look something like:
hello
goodbye
aufwiedersehn
goodnight
foreach val ( 1.0 to 10.0 step 0.5 )
echo val
end
This will increment val from 1.0 to 10.0 in steps of 0.5. The inner body of
the loop will be executed 19 times.
BUGS
Any bugs in the define code and macro handlers will probably show up
here.
SEE ALSO
The define command.
32
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
HELP
COMMAND
HELP
Online quick info facility.
SYNOPSIS
help [ command_name ]
DESCRIPTION
help examines the command name and lists the parameters of the specified
command and short description of each. This is useful to quickly jog the
memory of the particular parameter name desired for a command. There is
no extended description given. If no command name is given, the help
command lists all known commands.
BUGS
Some command parameters do not have a description. Also, the output
should be piped through more(1) àla the man command.
SEE ALSO
The man command.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
33
MAN
COMMAND
MAN
Online help facility for SUPREM-IV.
SYNOPSIS
man [ command_name ]
DESCRIPTION
man examines the command name and attempts to find a manual page for
that command. The manual pages are piped through more(1) for user
viewing.
Manual pages live in the man subdirectory of the home directory of
SUPREM-IV. The first location checked for manual pages is that given by
the environment variable MANDIR. If this fails, it checks in a default location defined in the program. The system administrator should have set
this for your system.
BUGS
The pipe to the more program is slow, ways to speed this and still make
use of the more program need to be investigated. The man command also
needs to have the exact name typed out or no help will be printed. This behavior is a little restrictive.
34
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MAN
SEE ALSO
The UNIX command – more(1).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
35
SET
COMMAND
SET
Set various shell parameters.
SYNOPSIS
set [ ( echo | noexecute | prompt string ) ]
DESCRIPTION
This command allows the user to turn on several useful shell parameters.
The command unset allows the same parameters to be turned off.
echo
The echo parameter causes the command buffer to be echoed to the standard output device. This is not necessary when commands are being entered interactively but useful when reading commands from a file.
noexecute
The noexecute flag will put all entered commands into check only mode.
If this flag is on, commands will only check for the legality of their arguments and not act upon them.
prompt
The prompt parameter takes the remainder of the line and uses it as the
prompt for the rest of the session. The default prompt is SUPREM4>.
36
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
SET
BUGS
The parameters all have to be typed in full. The parser does not understand
shortened versions.
SEE ALSO
The unset command.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
37
SOURCE
COMMAND
SOURCE
Execute commands from the specified file.
SYNOPSIS
source filename
DESCRIPTION
The source command allows users to read commands from a command
file. Commands are read from the file until an end of file mark is found.
This is especially useful for backgrounding large groups of commands.
The source command places the file in the current input stream. source
commands can be nested until the limit of open file descriptors (system dependent ~20). Several files are sourced at the beginning of the session.
The first is a system wide model file which contains defaults for the coefficients. The second and third are the home directory file by the name of
.supremrc and a local directory .supremrc. These files allow the user to
specify his own start up information and defaults.
BUGS
No known bugs.
38
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
UNDEF
COMMAND
UNDEF
Undefine previously defined macros.
SYNOPSIS
undef [ macro_name ]
DESCRIPTION
The undef command can be used to turn off previously defined macro.
macro_name and its expansion are deleted from the macro table. This
command is similar to the csh(1) unalias command.
BUGS
The command is open to macro substitution. The sequence:
define macro this is a macro
undef macro
will attempt to undefine the macro “this”. To be able to undefine any macro, the % must be the first character on the line.
SEE ALSO
The define command.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
39
UNSET
COMMAND
UNSET
Unset various shell parameters.
SYNOPSIS
unset [ ( echo | noexecute ) ]
DESCRIPTION
This command allows the user to turn off several useful shell parameters.
The command set allows the same parameters to be turned off.
echo
Turning off the echo option turns off echoing the command buffer. This is
usually the desired setting (and the default) when entering commands interactively as opposed to when commands are taken from a file.
noexecute
The noexecute flag when off sets all commands to normal mode. They
parse and examine parameters and will execute the command if they have
legal data.
BUGS
The parameters all have to be typed in full. The parser does not understand
shortened versions.
40
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
UNSET
SEE ALSO
The set command.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
41
UNSET
42
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Commands
DESCRIPTION
This is a brief introduction to the commands and their actions in
SUPREM-IV.GS. These are commands that usually have some action associated with them, as opposed to the models commands which typically
set coefficients.
There are several groups of commands in this section. The first are commands which are used for the input or output of data. The second are simulation commands which are the core of SUPREM-IV.GS. The third are
commands which are primarily for post processing. The remainder are
bunched in the aptly named miscellaneous category.
Data Input and Output Commands
boundary
This command allows the user to specify lines which are exposed to gas in
a rectangular grid.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
43
Commands
initialization
This command allows the user to set up the initial grid and specify background concentrations.
line
This command allows the user to position x and y grid lines for a rectangular mesh.
mode
This command allows the user to select a one or two dimensional simulation.
profile
This command allows the user to read in ASCII data file of depth and doping data.
region
The region command allows the user to specify which sections of the rectangular mesh are which material.
structure
The structure command allows the user to read and write mesh and solution values. This is the main method of inputting and outputting data to
and from the program.
Simulation Commands
etch
This command allows the user to etch layers.
44
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Commands
deposit
This command allows the user to deposit layers.
diffuse
This command allows the user to specify a time temperature step.
implant
This command allows the user to model an implant with either a Gaussian
or a Pearson-IV distribution.
method
This command allows the user to pick the numerical options for solving
the equations.
stress
This command computes the thermal elastic stresses.
Post Processing Commands
contour
This command allows the user to plot an isoconcentration line of the selected variable. It is usually used with the plot.2d statement.
label
This allows the user to place a label on the plot at a given location.
option
This command allows the user to pick the program’s verbosity level.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
45
Commands
plot.1d
This command allows the user to plot the selected variable in one dimensional cross sections through device.
plot.2d
This command allows the user to plot the outline and/or grid lines in the
two dimensional mesh. It is very useful for setting up the display for the
contours.
print.1d
This prints the information that a plot.1d would draw.
select
This command allows a variable to be chosen as the z coordinate for the
plot command to follow.
Miscellaneous Commands
cpulog
This command instructs the program to dump cpu statistics whenever it
feels like it.
echo
This command prints a string.
pause
This command waits for the user to input a command or a simple return.
46
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Commands
printf
This command passes each white space separated token to the expression
parser.
BUGS
See the individual command descriptions.
SEE ALSO
See the other command descriptions for more detail.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
47
BOUNDARY
COMMAND
BOUNDARY
Specify a surface type.
SYNOPSIS
boundary
( reflecting | exposed | backside )
xlo = <string> ylo = <string>
xhi = <string> yhi = <string>
DESCRIPTION
This statement is used to specify what conditions to apply at each surface
in a rectangular mesh.
reflecting | exposed | backside
At present, three surface types are recognized. exposed surfaces correspond to the top of the wafer. Materials are only deposited on exposed surfaces (so if a deposit does nothing you know where to start looking).
Impurity predeposition also happens at exposed surfaces, as does defect
recombination and generation. backside surfaces roughly correspond to a
nitride- or oxide-capped backside. Defect recombination and generation
happen here. reflecting surfaces correspond to the sides of the device, and
are also good for the backside if defects are not being simulated. The default for surfaces is reflecting.
48
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BOUNDARY
xlo, ylo, xhi, yhi
The bounds of the rectangle being specified. The <string> value should be
one of the tags created in a preceding line statement.
EXAMPLES
boundary exposed xlo=left xhi=right ylo=surf yhi=surf
boundary backsid xlo=left xhi=right ylo=back yhi=back
These lines specify that the top of the mesh is the exposed surface, and
that the bottom is the backside.
BUGS
The top surface should probably default to exposed, and the bottom to
backside. We took a poll, though, and decided it was safer that our users
knew about the existence of boundary codes.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
49
CONTOUR
COMMAND
CONTOUR
Plot contours in the selected variable on a two-dimensional plot.
SYNOPSIS
contour
[ line.type=<n> ] [ value=<n> ] [ symb=<n> ]
[ print ] [ label ]
DESCRIPTION
The contour statement draws a contour in the selected variable (see the
select statement) at the value specified. value must be specified in the
range of the computed variable. For instance, if plotting log boron, value
should be in the range 10 to 20 and not 1010 to 10 20. This statement assumes a plot.2d has been specified and the screen has been set up for plotting a two dimensional picture. If this has not been done, the routine will
probably produce garbage on the screen.
line.type
This allows the line type to be specified for this contour. The default is 1.
Different line types have different meanings to different graphics devices.
value
This floating parameter expresses the value that the contour line should be
plotted at. If boron had been selected, a value of 1016 would produce a line
of constant boron concentration of 1016 cm-3.
50
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
CONTOUR
symb
This integer parameter indicates that the contour line should be drawn
with symbols on the contour line. The integer value indicates different
symbols.
print
This boolean parameter instructs the contour command to print the line
segments coordinates rather than plot them. This is useful for exporting
data to other programs and plot software.
label
The command will attempt to place a text string on the contour in an ideal
location to label the value.
EXAMPLES
contour val=1e10
This command will draw a line at a isoconcentration of 1×1010.
BUGS
This should probably check to make sure a plot.2d has been done. It is
conceivable that this statement could produce floating point exceptions
when a plot.2d has not been done. This is, to put it mildly, annoying. Plot
software bugs will show up in this command.
SEE ALSO
The plot.2d and for commands.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
51
CPULOG
COMMAND
CPULOG
Log the cpu usage summary to a file.
SYNOPSIS
cpu [ log ] [ cpufile=<string> ]
DESCRIPTION
The cpulog statement allows the user to get a summary of cpu usage by
the program. The user can select this information to appear on his terminal
or have it sent to the standard output. Most of the cpu intensive routines
will report to the user the time used.
log
This option specifies whether to start or stop cpu usage logging. A true
value enables cpu usage logging, false turns it off. The default is true.
cpufile
This string parameter allows the user to select a file name for the output of
cpu usage. The default is to the standard output.
EXAMPLES
cpu log
This command enables cpu reporting to the screen.
52
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
CPULOG
cpu log file=foo
This enables the cpu statistics reporting and stores them in file foo.
BUGS
The cpu usage statistics of an algorithm are only as complete as the programmer who implemented the algorithm. The times can be no more accurate than the reporting on the machine the code is running on. This is
typically a sixtieth of a second, but may vary. (For example, the Cray
X-MP/4 uses 9.5 nanoseconds).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
53
DEPOSIT
COMMAND
DEPOSIT
Deposit a layer.
SYNOPSIS
deposit
( silicon | oxide | oxynitr | nitride | poly | photores |
alumin | gaas )
thickness = <n> [ divisions = <n> ]
[ none | arsenic | antimony | boron | phosphor |
beryllium | magnesium | selenium | isilicon |
tin | germanium | zinc | carbon | generic]
[ conc=<n> ] [ space=<n> ]
[ file=<string> ]
DESCRIPTION
This statement provides a primitive deposition capability. Material is deposited on the “exposed” surface of the structure, and its upper surface becomes the new exposed surface. This code is now based on the
generalized triangulation package originally written by Conor Rafferty as
a stand-alone program, tri. This tends to be significantly more robust than
the grid generation algorithm in earlier versions of SUPREM-IV (e.g.
8912). There have also been several enhancements in the handling of the
offset line. It is now possible, for instance, to fill a trench completely.
silicon | oxide | oxynitr | nitride | poly | photores | alumin | gaas
The material to be deposited.
54
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
DEPOSIT
thickness
The thickness in microns.
divisions
The number of vertical grid spacings in the layer, default 1.
none | arsenic | antimony | boron | phosphor | beryllium |
magnesium | selenium | isilicon | tin | germanium | zinc |
carbon | generic
The type of doping in the deposited layer.
conc
This floating point parameter specifies the level of the doping in the deposited layer.
space
This floating point parameter represents the average spacing between
points along the outside edge of the deposit.
file
This string parameter specifies the name of a file that contains a string that
contains the coordinates associated with the deposit surface. This file
could be generated using a topography simulator such as SAMPLE.
EXAMPLES
deposit oxide thick=0.02
This deposits silicon dioxide 200 angstroms thick on the surface of the silicon.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
55
DEPOSIT
BUGS
Only uniform grid in the deposited material.
Occasionally makes grid errors in following the surface.
The offset profile is not based on any physical model.
SEE ALSO
The etch statement.
56
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
DIFFUSE
COMMAND
DIFFUSE
Run a time temperature step on the wafer and calculate oxidation and diffusion of impurities.
SYNOPSIS
diffuse
time=<n> temperature=<n>
[ ( dryo2 | weto2 | nitrogen | ammonia | argon |
antimony | arsenic | boron | phosphorus |
beryllium | magnesium | selenium | isilicon |
tin | germanium | zinc | carbon | generic ) ]
[ gas.conc=<n> ] [ pressure=<n> ]
[ gold.surf ] [ continue ]
[ movie=<string> ] [ dump=<n> ]
DESCRIPTION
The diffuse statement allows the user to specify a diffusion or oxidation
step. Any impurities present in the wafer are diffused. If the wafer is exposed to a gas, a predeposition or oxidation can be performed. This statement represents the core simulation capability of SUPREM-IV. Users can
expect that this statement will take a lot of CPU time.
The parameters for oxidation and diffusivities can be found on the statements in the models section of the manual. Refer to either the oxide statement or any of the impurity statements to determine how to change
coefficients of the models.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
57
DIFFUSE
time
This parameter represents the amount of time the wafer will spend in the
furnace in minutes.
temp
This parameter allows specification of the furnace temperature in degrees
centigrade.
antimony, arsenic, boron, phosphorus, beryllium, magnesium,
selenium, silicon, tin, germanium, zinc, carbon, generic
The above switched booleans of gas types allow the user to specify the
type of impurity that may be in the gas stream. The value of gas.conc applies to these gas types. Only one gas type may be specified per diffusion
step.
dryo2 weto2 nitrogen ammonia argon
The above switched booleans of gas types allow the user to specify the
type of gas present in the furnace during the diffusion step. These gas
types are not affected by the gas.conc parameter. Only one gas type may
be specified per diffusion step. There is currently no difference between
nitrogen, argon, and ammonia.
gas.conc
This allows the user to specify the gas concentration of an impurity during
preepositions, in atoms per cubic centimeter.
pressure
This is the partial pressure of the active species, in atmospheres. It defaults
to 1 for both wet and dry oxidation.
58
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
DIFFUSE
gold.surf
This floating point parameter specifies the gettered gold concentration value as a sink. It is used for the gettering model described on the gold command.
continue
This specifies a continuing diffusion. Do not reset the total time to 0, do
not reset the analytic oxide thickness to the default value of “initial” on the
oxide command, and do not initialize the defects.
movie
This character string parameter should be made up of SUPREM-IV commands. They will be executed at the beginning of each time step. It is typically used to produce plots of a variable as a function of time during the
diffusion process. Any legal SUPREM-IV command can be specified in
the string. The variable time is set by the movie routine. Consequently,
time will be expanded as a macro for use in plot labels or print outs.
dump
This parameter instructs the simulator to output files on after every n’th
time step. The files will be structure files and will be readable with the
structure statement. The names will be of the form s.time, where time is
the current total time of the simulation.
EXAMPLES
diffuse time=30 temp=1000 boron gas.conc=1.e20
This statement specifies that a 1000˚C, 30 minute, boron predeposition is
to be performed.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
59
DIFFUSE
diffuse time=30 temp=1000 dryo2
This statement instructs the simulator to grow oxide for 30 minutes at
1000˚C in a dry oxygen ambient.
diffuse time=30 temp=1000 movie="select z=log10(bor);
plot.1d x.v=1.0;"
This command instructs SUPREM-IV to do a 30 minute, 1000˚C diffusion. Before each time step, the current boron concentration will be plotted
along a horizontal slice 1.0µm into the wafer. (See select, plot.1d).
diffuse time=30 temp=1100
movie="select z=doping;
printf Time is: time yfn(0.0, 0.0) sil@oxi(0.0)"
This command instructs SUPREM-IV to do a 30 minute, 1000˚C diffusion. Before each time step, the total net active doping concentration is
chosen as the plot z variable. The printf statement will then print the string
“Time is:”, the current time of the diffusion in seconds, the y value along a
vertical slice at x = 0.0 where the doping is equal to zero (i.e. the junction),
and the location of the silicon oxide interface in the vertical slice at
x = 0.0.
BUGS
There can still be occasional convergence problems. If these occur when
defects are being computed, they can usually be fixed by performing a
complete LU decomposition instead of a partial. Use the “method full”
command to achieve this.
The models implemented in the diffusion and oxidation are involved in
ongoing research. Disagreements between simulation and experiment is
possible. This can be due to the differences in processing conditions be-
60
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
DIFFUSE
tween the lab where the original experiment was performed and your lab,
or due to model shortcomings.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interst, magnesium, material, method, oxide, phosphorus, selenium,
silicon, tin, trap, vacancy, and zinc commands.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
61
ECHO
COMMAND
ECHO
A string printer and desk calculator.
SYNOPSIS
echo [ string ]
DESCRIPTION
This command merely prints the string given to it. This is useful for placing comments in an output file. The command attempts to parse the string
to a legal real number if possible. It has a regular expression parser builtin. This allows echo to be used as a desk calculator.
EXAMPLES
echo jimmin at the jimjam frippin at the frotz
This will send the string
jimmin at the jimjam frippin at the frotz
to standard out.
echo (2^3^4)
4096
62
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ECHO
echo ( 15.0 - 12.0 * exp( 4.0 - 2.0 / 6.0 ) )
This will print the result of the arithmetic expression, which is of course,
8.373.
BUGS
No known bugs.
SEE ALSO
The UNIX command – more(1).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
63
ETCH
COMMAND
ETCH
Etch a layer.
SYNOPSIS
etch
[ silicon | oxide | oxynitr | nitride | poly | photores |
alumin | gaas ]
[ left | right | start | continue | done | dry | all ]
[ x=<n> ] [ y=<n> ] [ thick=<n> ]
[ p1.x=<n> ] [ p1.y=<n> ] [ p2.x=<n> ] [ p2.y=<n> ]
[ file=<string> ]
DESCRIPTION
This statement provides an etching capability. Material is etched from the
structure, and the underlying regions are marked as the “exposed” surface.
The etch shape can be described in several different ways. The user must
specify the final shape of the region to be etched, there is no capability at
present to simulate the etch region shape.
silicon, oxide, oxynitr, nitride, poly, photores, alumin, gaas
The material to be etched. If a material is specified, only that material is
etched even if other materials lie within the etch region. If no material is
specified, all materials in the etch region are removed.
64
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ETCH
left, right
These provide the user with a quick means of doing trapezoidal shaped
etches. The etch region is to the left / right of the line specified by the coordinates given in p1.x, p1.y and p2.x, p2.y.
start, continue, done
This allows the user to specify an arbitrarily complex region to be etched.
Several lines can be combined to specify the several points that make up
the region. See the examples.
dry
This parameter indicates that the etch shape should be a replica of the current surface, but straight down “thickness” microns.
all
All of the specified material is removed.
x, y
These parameters allow the user to specify point in the start / continue /
done mode of etch region specification.
p1.x, p1.y, p2.x, p2.y
These parameters allow the specification of a line for left / right etching.
thick
This parameter allows specification of a thickness for the dry etch type.
file
This string parameter specifies the name of a file that contains a string that
contains the coordinates associated with the etched surface. This file could
be generated using a topography simulator such as SAMPLE.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
65
ETCH
EXAMPLES
etch nitride left p1.x = 0.5 p1.y=0.0 p2.x=0.5 p2.y=-1.0
This command etches all the nitride left of a vertical line at 0.5.
etch oxide start x=0.0 y=0.0
etch continue x=1.0 y=0.0
etch continue x=1.0 y=1.0
etch done x=0.0 y=1.0
This etches the oxide in the square defined at (0,0), (1,0), (1,1), and (1,0).
etch dry thick=0.1
This etch will find the exposed surface, lower it straight down 0.1µm and
this line will be the new surface.
BUGS
Uses no physical model.
This code is sensitive to grid placement. It often helps to prepare the substrate by having a vertical grid line at the foot of the etched part of a deposited layer. Otherwise a fascinating ripped nylon mesh is generated.
Contrary to what some commercial vendors maintain, the mesh produced
is the best possible one to solve PDE’s given the constraints. However, It
is usually better to place a line at the etch locations.
The code currently does distinguish between surface and subsurface materials. “Etch silicon left p1.x=0.2” will etch the silicon to the left of 0.2µm,
including the substrate. Use the start / cont / end sequence to work
around this.
66
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
IMPLANT
COMMAND
IMPLANT
Perform ion implantation.
SYNOPSIS
implant
( antimony | arsenic | boron | bf2 | cesium | phosphorus |
beryllium | magnesium | selenium | isilicon | tin |
germanium | zinc | carbon | generic )
[ gauss | pearson ]
dose=<n> energy=<n>
[ damage ] [ max.damage=<n> ]
[ range=<n> ] [ std.dev=<n> ]
[ gamma=<n> ] [ kurtosis=<n> ]
[ angle=<n> ]
DESCRIPTION
This statement is used to simulate ion implantation. There are two different types of analytic models available. The first implements a simple
Gaussian distribution. The second uses the moments data file to compute a
Pearson-IV distribution. These models are only as good as the data in the
files. The file data can be overridden by directly specifying the appropriate
values on the implant command line.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
67
IMPLANT
antimony, arsenic, boron, bf2, cesium, phosphorus, beryllium |
magnesium | selenium | isilicon | tin | germanium | zinc |
carbon
These parameters specify the impurity to be implanted. Default data for
the range statistics exists only for antimony, arsenic, boron, BF2, phosphorus, beryllium, magnesium, selenium, isilicon, tin, germanium, zinc, and
carbon.
gauss, pearson
These parameters specify which type of distribution is being used. A Pearson-IV distribution is the default.
dose
This parameter allows the user to specify the dose of the implant. The
units are in atoms/cm2.
energy
This parameter specifies the implant energy in KeV.
damage
This parameter indicates that a computation of the damage due to the implant should be performed. The data is from Hobler and Selberherr [1] and
exist only for antimony, arsenic, boron, and phosphorus.
max.damage
The maximum amount of damage to the crystal that makes sense to calculate. Clearly damage above the crystal density is absurd.
range, std.dev, gamma, kurtosis
These parameters allow the user to override the table values. The full set
of data has to be given. It is not possible, for instance, to override only the
68
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
IMPLANT
range parameter. The gamma and kurtosis variables only have meaning
for the Pearson-IV distribution.
angle
This parameter allows the user to specify the angle normal to the substrate
that the impurity was implanted at.
EXAMPLES
implant phosph dose=1e14 energy=100 pearson
This statement specifies that a 100KeV implant of phosphorus was done
with a dose of 1×1014 cm-2. The Pearson-IV model is to be used for the
distribution function.
implant phos dose=1e14 range=0.1 std.dev=0.02 gauss
This statement specifies an implant of phosphorus was done with a dose of
1×1014 cm-2. The Gaussian model is to be used for the distribution function. The range and standard deviation are specified in microns instead of
using table values.
implant phosph dose=1e14 energy=100 pearson damage
This statement specifies that a 100KeV implant of phosphorus was done
with a dose of 1×1014 cm-2. The Pearson-IV model is to be used for the
distribution function. The damage from this implant is calculated and
stored as point defects.
BUGS
Very high angle implants may have non-physical profiles near the device
edges.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
69
IMPLANT
Occasionally problems are encountered on undercut surfaces and other reentrant shapes. The algorithm really wasn't intended for these types of
shapes.
REFERENCES
1. G. Hobler and S. Selberherr, “Two-Dimensional Modeling of Ion Im-
plantation Induced Point Defects,” IEEE Trans. on CAD, 7(2), p. 174,
1988.
70
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INITIALIZE
COMMAND
INITIALIZE
Setup grid, background doping levels.
SYNOPSIS
initialize
[ infile=<string> ]
[ ( antimony | arsenic | boron | phosphorus | gold |
gallium | beryllium | magnesium | selenium |
isilicon | tin | germanium | zinc | carbon | generic ) ]
[ conc=<n> ]
[ orientation=<n> ]
[ line.data ] [ scale ] [ flip.y ]
DESCRIPTION
The initialize statement sets up the mesh from either a rectangular specification or a from a previous structure file. The statement also initializes the
background doping concentration.
infile
The infile parameter selects the file name for reading. The file must contain a previously saved structure, see the structure command. A generated
grid using tri may also be input at this point. If no filename is specified,
the program will finish generating a rectangular mesh.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
71
INITIALIZE
antimony, arsenic, beryllium, boron, carbon, generic,
germanium, gold, magnesium, phosphorus, selenium, isilicon,
tin, zinc
These parameters specify the type of impurity that forms the background
doping.
conc
This parameter allows the user to specify the background concentration in
cm-3.
orientation
This parameter allows the user to specify the substrate orientation. Only
100, 110 and 111 are recognized.
line.data
This boolean parameter indicates that the locations of mesh lines should
be listed.
scale
Parameter to scale the size of an incoming mesh. The default is 1.0.
flip.y
This boolean parameter indicates if the mesh should be flipped around the
x axis. If is sometimes useful for reading grids prepared with tri or other
grid generation programs.
EXAMPLES
init infile=foo
This command reads in a previously saved structure in file foo.
72
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INITIALIZE
initialize conc=1e15 boron
This command finishes a rectangular mesh and sets up with boron doping
of 1×1015 cm-2.
BUGS
There are no known bugs.
SEE ALSO
The bound, line, region, structure statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
73
LABEL
COMMAND
LABEL
Put labels on a plot.
SYNOPSIS
label
[ x=<n> y=<n> ] [ label=<string> ] [ symb=<n> ]
[ line.type=<n> ]
DESCRIPTION
The label command allows the user to put random pieces of text anywhere
on a SUPREM-IV plot.
x, y
Where to put the label, in microns.
label
What string to print.
symb, line.type
These parameters will draw a short line of the specified linetype or a symbol of the specified number in front of the text. Useful for labelling contours, for instance.
74
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
LABEL
EXAMPLES
label label="Arsenic" line=3
label label="Phosphorus" line=4
These commands will put two labels on the plot at a position specified by
the mouse.
label label="This is Interesting, eh?" x=10.0 y=10.0
This will place the string, centered, at the location (10, 10).
BUGS
There are no known bugs.
SEE ALSO
The plot.1d, plot.2d, and for statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
75
LINE
COMMAND
LINE
Specify a mesh line location.
SYNOPSIS
line ( x | y | z ) location = <n> [spacing = <n>] [tag = <string>]
DESCRIPTION
This statement is used to specify the position and spacing of mesh lines.
All line statements should come before region and boundary statements,
which should in turn be followed by an initialize statement.
Only flat structures can be specified with line / region / boundary statements. To create the grid for a more complicated structure, use the interactive grid generator skel.
x|y|z
A mesh line is either horizontal, vertical, or into the screen. The x coordinate increases from left to right. The y coordinate increases into the substrate, that is, from top to bottom. People who learned analytic geometry
with the y axis pointing up seem to find this confusing. The z coordinate is
supported, somewhat. Rectangular grid generation in three dimensions is
the only three dimensional part of the program. It is anticipated that the
next release will be fully one, two, and three dimensional.
location
The location along the chosen axis, in microns.
76
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
LINE
spacing
The local grid spacing, in microns. SUPREM-IV will add mesh lines to
the ones given according to the following recipe. Each user line has a
spacing, either specified by the user or inferred from the nearest neighbor.
These spacings are then smoothed out so no adjacent intervals will have a
ratio greater than 1.5. New grid lines are then introduced so that the line
spacing varies geometrically from the user spacing at one end of each interval to that at the other. The example below might alleviate the confusion you must be experiencing.
tag
Lines can be tagged with a label for later reference by boundary and region statements. The label is any word you like.
EXAMPLES
line x loc=0 spa=1 tag=left
line x loc=1 spa=0.1
line x loc=2 spa=1 tag=right
line y loc=0 spa=0.02 tag=surf
line y loc=3 spa=0.5 tag=back
There are three user-specified x lines and two user y lines. Taking the x
lines for illustration, there is finer spacing in the center than at the edges.
After processing, SUPREM-IV produces a mesh with x lines at 0.0, 0.42,
0.69, 0.88, 1.0, 1.12, 1.31, 1.58, and 2.0µm. Around the center, the spacing is 0.12, approximately what was requested. At the edge, the spacing is
0.42µm, because that was as coarse as it could get without having an interval ratio greater than 1.5. If the interval ratio was allowed to be 9, say, then
we would have got one interval of 0.9µm and one interval of 0.1µm on
each side. In this example, specifying a spacing of 1µm at the edges was
redundant, because that's what the spacing of the user lines was anyway.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
77
LINE
BUGS
It's hard to guess how many lines are going to be generated in each interval.
Coarse spacings are sometimes rounded down by the smoothing algorithm
in an undesirable way, creating too many grid points.
Automatic re-grid has been broken since oxidation introduced moving
boundaries. Therefore the initial mesh specification is quite important to
the success of the simulation. Use “best guess” numbers for the profiles, or
coarse-grid simulations, to get a feel for the required spacings in the initial
and final profile.
78
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
METHOD
COMMAND
METHOD
Select numerical methods and models for diffusion and oxidation.
SYNOPSIS
method
[ ( vacancies | interstitial | arsenic | phosphorus |
antimony | boron | gallium | oxidant | velocity |
traps | gold | psi | cesium | beryllium | magnesium |
selenium | isilicon | tin | germanium | zinc | carbon |
generic ) ]
[ rel.error=<n> ] [ abs.error=<n> ]
[ init.time=<n> ] [ ( trbdf | formula ) ]
[ min.fill ] [ min.freq=<n> ]
[ ( gauss | cg ) ] [ back=<n> ] [ blk.itlim=<n> ]
[ ( time | error | newton ) ]
[ ( diag | full.fac ) ]
[ ( fermi | two.dim | steady | full.cpl ) ]
[ ( erfc | erfg | erf1 | erf2 | vertical | compress | viscous ) ]
[ grid.oxide=<n> ] [ skip.sil ]
[ oxide.gdt=<n> ] [ redo.oxide=<n> ]
[ oxide.early=<n> ] [ oxide.late=<n> ] [ oxide.rel=<n> ]
[ gloop.emin=<n> ] [ gloop.emax=<n> ] [ gloop.imin=<n> ]
DESCRIPTION
This statement sets the flags for selection of algorithm for various mathematical solutions. The statement also allows the user to select the com-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
79
METHOD
plexity desired for the diffusion and oxidation models. Appropriate
defaults for the numerical parameters are included in the model start up
file so users should only have to specify the type of model desired for the
diffusion and oxidation. The numerical methods used in SUPREM-IV for
solution of the diffusion equations are described in more detail in Law and
Dutton [1].
vacancies, interstitial, arsenic, phosphorus, antimony, boron,
gallium, oxidant, velocity, traps, gold, psi, beryllium,
magnesium, selenium, isilicon, tin, germanium, zinc, carbon,
generic
These options allow the user to specify a single impurity. The error bound
parameters are specific for each impurity. If error bounds are listed, an impurity must also be selected.
rel.err
This parameter indicates the precision with which the impurity block must
be solved. In general, the error will be less that half of the indicated error
since the program is conservative in its error estimates. The defaults are
0.01 for all impurities except the potential which is solved to 0.001.
abs.err
This parameter indicates the size of the absolute value of the error. For the
dopants, the absolute error defaults to 10 9. For defects, the absolute error
defaults to 10 5. For the potential, the error defaults to 10 -6.
init.time
This parameter specifies the size of the initial time step. It defaults to 0.1
seconds. A routine to estimate the initial time step is being worked on.
80
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
METHOD
trbdf, formula
These parameters specify the method of time integration to be used. The
trbdf option indicates a combination trapezoidal rule/backward difference
should be used. The error is estimated using Milne’s device. The formula
method allows the user to specify the time step directly as a function of
time ( t ), previous time step ( dt ) and grid time ( gdt ). This option is primarily for testing. The trbdf method is the default. The time step methods
have been taken from literature, see Yeager and Dutton [2] and Bank et al.
[3].
min.fill, min.freq
This option allows the user to specify a minimum fill. It defaults to true.
This is a highly recommended option since it can reduce the matrix sizes
by a factor of two or more. The size of the matrix is proportional to speed.
min.freq is a parameter which controls the frequency of min fill reorder-
ing. It is only partially implemented and will have no effect on the calculation.
gauss, cg
These parameters allow the user to specify the type of iteration performed
on the linear system as a whole. gauss specifies that this iteration should
be Gauss-Seidel, cg specifies that a conjugate residual should be used. The
default is cg. The gauss option is considerably slower, it should be deleted in the future. The CG algorithm is described by Elman [4].
back
This integer parameter specifies the number of back vectors that can be
used in the cg outer iteration. The default is 3, and the maximum that can
be used is 5. The higher the number, the better the convergence and the
more memory used.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
81
METHOD
blk.itlim
The maximum number of block iterations that can be taken. The block iteration will finish at this point independent of convergence.
time, error, newton
These parameters specify the frequency with which the matrix should be
re-factored. The time parameter specifies that the matrix should be re-factored twice per time step. This option takes advantage of the similarity in
the matrix across a time integration. The error option indicates the matrix
should be re-factored whenever the error in that block is decreasing. The
newton option will force the re-factorization at every newton step. The
default is time.
diag, full.fac
These parameters specify the amount of fill to be included in the factorization of the matrix. full.fac indicates that the entire amount of fill is to be
computed. The diag option indicates that the only the diagonal blocks
should be factored in the matrix. The diag option is the default, although
under certain conditions (one dimensional) full.fac may perform better.
fermi, two.dim, steady, full.cpl
These parameters specify the type of defect model to be used. The fermi
option indicates that the defects are assumed to be a function of the fermi
level only. The two.dim option indicates that a full time dependent transient simulation should be performed. The steady option indicates that the
defects can be assumed to be in steady state. The full.cpl option indicates
that the full coupling between defects and dopants should be included. The
default is fermi.
erfc, erfg, erf1, erf2, vertical, compress, viscous
These are oxide model parameters. The erfc option indicates that a simple
error function approximation to a bird's beak shape should be used. The
82
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
METHOD
erf1 and erf2 models are analytic approximations to the bird's beak from
the literature (see the oxide statement). The erfg model chooses whichever of erf1 or erf2 is most appropriate. The vertical model indicates that the
oxidant should be solved for and that the growth is entirely vertical. The
compress model treats the oxide as a compressible liquid. The viscous
model treats the oxide as an incompressible viscous liquid. Real oxide is
believed to be incompressible, but the compressible model is a lot faster.
It's an accuracy vs. speed trade-off.
grid.oxide
This parameter is the desired thickness of grid layers to be added to the
growing oxide. The value is specified in microns. It represents the desired
thickness of grid layers to be added to the growing oxide, in microns. It
has a side effect on time steps (see oxide.gdt).
skip.sil
This boolean parameter indicates whether or not to compute stress in the
silicon. The default is false. The calculation can only performed when the
viscous oxide model is used. The silicon substrate is treated as an elastic
solid subject to the tractions generated by the oxide flow. It should not be
turned on indiscriminately, since the silicon grid is generally much larger
than the oxide grid, and the stress calculation correspondingly more expensive.
oxide.gdt
The time step may be limited by oxidation as well as diffusion; the oxide
limit is specified as a fraction (oxide.gdt) of the time required to oxidize
the thickness of one grid layer (grid.oxide).
redo.oxide
To save time, the oxide flow field need not be computed every time the diffusion equation for impurities is solved. The parameter redo.oxide speci-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
83
METHOD
fies the percentage of the time required to oxidize the thickness of one grid
layer which should elapse before resolving the flow field. Usually redo.oxide is much less than oxide.gdt, which is an upper bound on how
long the solution should wait. It is mainly intended to exclude solving oxidation at each and every one of the first few millisecond time steps when
defects are being tracked.
oxide.early, oxide.late, oxide.rel
These parameters are not normally modified by users. They relate to internal numerical mechanisms, and are described only for completeness. A
node whose spacing decreases proportionally by more than oxide.late is
marked for removal. If there any nodes being removed, then in addition all
nodes greater than oxide.early are removed. The default values are oxide.early = 0.5 and oxide.late = 0.9. For earlier node removal (less obtuse
triangles), try oxide.late = 0.3 and oxide.early = 0.1. It makes no sense,
but does no harm, to have oxide.early greater than oxide.late. The oxide.rel parameter is the solution tolerance in the nonlinear viscous model.
The default is 10-6 (that is, a 10-4 percentage error in the velocities). It can
be increased for a faster solution, but a value greater than about 10-3 will
probably give meaningless results.
gloop.emin, gloop.emax, gloop.imin
This group of parameters controls loop detection during grid manipulation. The loop detection checks for intrusions and extrusions in the boundary. The intrusion-fixing algorithm is triggered by angles greater than
gloop.imin. The default value is gloop.imin = 170˚. A larger value means
that more extreme intrusions can develop and increases the possibility of a
tangled grid. A smaller value leads to earlier intrusion-fixing; too small a
value will lead to inaccuracy due to premature intervention. Similar concerns apply to the other parameters. The values are a compromise between
safety and accuracy. The extrusion-fixing algorithm is always triggered by
angles greater than gloop.emax. Again, the default is 170˚. In addition, it
84
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
METHOD
be triggered by lesser extrusions, anything greater than gloop.emin, if the
extrusion is a single-triangle glitch in the boundary. The default value is
gloop.emin = 120˚. None of these parameters should be less than 90˚, because then the rectangular edges of the simulation space would be
smoothed out!
EXAMPLES
method arsenic rel.err=0.01 abs.err=1.0e9
This command indicates that the arsenic equation should be solved with a
relative error of 1% and concentrations below 1×109 can be ignored.
method min.fill cg back=3 init.ti=0.1 trbdf fermi vert
skip.sil=f
This command specifies that minimum fill reordering should be done and
that the entire system should be solved using a conjugate residual technique with three back vectors. The initial time step should be 0.1 seconds
and time should be integrated using the trbdf model. The fermi model
should be assumed for the defects and the vertical model for the oxide
growth. The stresses and potential and the silicon should not be computed.
BUGS
It is unclear if the numbering scheme provided by min.fill is optimal. More
research needs to be done here, especially for band ordering on vector machines. The only need for user intervention here should be to change the
oxidation and defect models.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
85
METHOD
REFERENCES
1. M.E. Law and R.W. Dutton, “Verification of Analytic Point Defect
Models using SUPREM-IV,” IEEE Trans. on CAD, 7(2), p. 181, 1988.
2. H.R. Yeager and R.W. Dutton, “An Approach to Solving Multi-Particle
Diffusion Exhibiting Nonlinear Stiff Coupling,” IEEE Trans. on Elec.
Dev., 32(10), p. 1964-1976, 1985.
3. R.E. Bank, W.M. Coughran, W. Fichtner, E.H. Grosse, D.J. Rose and
R.K. Smith, “Transient Simulation of Silicon Devices and Circuits,”
IEEE Trans. on Electron Devices, ED-32, p. 1992, 1985.
4. H.C. Elman, Preconditioned Conjugate Gradient Methods for Nonsymmetric Systems of Linear Equations, Yale University Research Report,
1981.
86
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MODE
COMMAND
MODE
Set the dimensionality of the simulator.
SYNOPSIS
mode [ one.dim | two.dim ]
DESCRIPTION
The mode statement determines the dimensionality of the simulator. The
internal data structure is changed slightly to support true one dimensional
mode operation when one dimension is selected. Two dimensions is the
default, and is the original operation mode.
one.dim, two.dim
These parameters set the simulator dimensionality.
BUGS
None.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
87
OPTION
COMMAND
OPTION
option – Set options.
SYNOPSIS
option [ quiet | normal | chat | barf ]
DESCRIPTION
The option statement used to be considerably more complicated. The plot
software now comes configured for X workstations. This command specifies only the verbosity of the simulator.
quiet, normal, chat, barf
These parameters determine the amount of information that is output to
the user about errors, cpu times, behavior of the algorithms, etc. The default is normal. The chat and barf modes are mainly useful for debugging
and would not normally be chosen by any user in their right mind.
BUGS
None – but the stuff printed isn't always what is needed.
88
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PAUSE
COMMAND
PAUSE
Wait and execute command.
SYNOPSIS
pause
DESCRIPTION
This command will stop the program and ask the user for input. The user
may type any legal SUPREM-IV command string to be executed. This is
useful for breaking up long input scripts to check the status, or placing in
the movie parameter of a diffuse command to check the progress of the
diffusion.
EXAMPLES
pause
The program will stop, print:
Type <RETURN> to continue, or a command to be executed:
and will wait for the user to respond.
BUGS
No known bugs.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
89
PLOT.1D
COMMAND
PLOT.1D
Plot a one dimensional cross section.
SYNOPSIS
plot.1d
[ (x.value=<n> | y.value=<n>) ]
[ exposed | backside | reflect | silicon | oxide |
nitride | poly | oxynitride | aluminum |
photoresist | gaas | gas ]
[ /exposed | /backside | /reflect | /silicon | /oxide |
/nitride | /poly | /oxynitride | /aluminum |
/photoresist | /gaas | /gas ]
[ boundary ] [ axis ] [ clear ]
[ symb=<n> ]
[ x.max=<n> ] [ x.min=<n> ] [ y.max=<n> ] [ y.min=<n> ]
[ arclength ]
DESCRIPTION
The plot.1d statement allows the user to plot cross sections vertically or
horizontally through the device. The statement has options to provide for
initialization of the graphics device and plotting of axes. The statement
can optionally draw vertical lines whenever a material boundary is
crossed. The vertical axis is the variable that was selected (see the select
statement). The plot can have limits given to it so that only a portion of the
entire device will be shown, or more than one variable can be conveniently plotted.
90
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PLOT.1D
The options and their action are described below:
x.value, y.value
These parameters specify that the cross section is to be done at a constant
value as specified by the parameter. This parameter value is in microns.
Only one of x.value or y.value can be specified for a given device. Specifying x.value will produce a vertical slice through the device and y.value
will specify a horizontal slice. An easy way to remember is that the cross
section is taken at the constant value specified. In one dimensional mode
these parameters do not need to be specified.
silicon | oxide | nitride … /silicon | /oxide | /nitride
In addition to constant x or y cross sections, a one-dimensional plot can be
generated along an interface. The interface lies between material 1, named
without an initial “/”, and material 2, named with a leading “/”. For example, “plot.1d oxide /silicon” shows the values in the oxide at the oxide/silicon interface. Thus “plot.1d oxide /silicon” will usually show something
different from “plot.1d silicon /oxide”. The backside, reflecting or exposed
surfaces of a material can be specified with the appropriate parameter. The
ordinate on the axis is the x coordinate of the points along the interface. If
the optional parameter arclength is set, the ordinate is instead the arc
length along the boundary from the leftmost point on the curve. The leftmost point itself has ordinate equal to its x coordinate in the mesh.
boundary
This parameter specifies that any material boundaries that are crossed
should be drawn in as vertical lines on the plot. It defaults false.
axis
This parameter specifies that the axes should be drawn. If this parameter is
set false and clear is false, the plot will be drawn on a top of the previous
axes. It defaults true.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
91
PLOT.1D
clear
The clear parameter specifies whether the graphics screen should be
cleared before the graph is drawn. If true, the screen is cleared. It defaults
true.
symb
This parameter allows the user to specify a symbol type to be drawn on the
cross sectional line. Each point is drawn with the specified symbol.
symb = 0 means no symbol should be drawn. It defaults to 0. symb = 1
and higher will add one of the predefined symbols to the plot.
x.max, x.min
These parameters allow the user to specify the range of the x axis. The
units are in microns and the default is the length of the device in the appropriate direction of the cross section.
y.max, y.min
These parameters allow the user to specify a range for the plot variable.
The values have to be in units of the selected variable. If log of the boron
concentration was selected, the values for this should be 16 and 10 to see
the concentrations between 1016 and 1010.
arclength
If this parameter is set, the ordinate is the arc length along the boundary
from the leftmost point on the curve. The leftmost point itself has ordinate
equal to its x coordinate in the mesh. This parameter only has meaning
when used with a plot along an interface.
92
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PLOT.1D
EXAMPLES
plot.1d x.v=1.0 symb=1 axis clear
This command will clear the screen, draw a set of axes, and draw the data
cross section at x = 1.0µm. Each point will be drawn with symbol 1.
plot.1d x.v=2.0 axis=f clear=f
This command draws a cross section at x = 2.0µm on the previous set of
axes.
plot.1d sil /oxi
Plots the selected variable along the silicon interface facing oxide.
BUGS
If arclength is set, and the interface between two materials comprises several disconnected pieces, the end of one arc is joined incorrectly to the
start of the next.
If arclength is set, the interface between materials is usually ordered leftto-right, but it is possible to confuse the routine, and get right-to-left.
There is no way to specify a line at a fixed distance from an interface.
There is no simple way to follow the “upper” surface of a layer if it has
several different layers on top of it.
SEE ALSO
The select statement.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
93
PLOT.2D
COMMAND
PLOT.2D
Plot a two dimensional xy picture.
SYNOPSIS
plot.2d
[ x.max=<n> ] [ x.min=<n> ] [ y.min=<n> ] [ y.max=<n> ]
[ clear ] [ fill ] [ boundary ] [ grid ] [ axis ]
[ vornoi ] [ diamonds ]
[ stress ] [ vmax=<n> ] [ vleng=<n> ]
[ flow ]
DESCRIPTION
The plot.2d statement allows the user to prepare a two dimensional xy
plot. This routine does not plot any solution values, however, it can prepare the screen for isoconcentration lines to be plotted. The statement can
draw the xy space of the device, label it, draw material boundaries, and
draw stress and flow vectors. If in one dimensional mode, it will return and
print an error message.
x.min, x.max
These parameters allow the user to specify a subset of the x axis to be plotted. The parameters will default to the current device limits. The units are
in microns.
94
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PLOT.2D
y.min, y.max
These parameters allow the user to specify a subset of the y axis to be plotted. The parameters will default to the current device limits. The units are
in microns.
clear
The clear parameter specifies whether the graphics screen should be
cleared before the graph is drawn. If true, the screen is cleared. It defaults
to true.
fill
The fill parameter specifies that the device should be drawn with the proper aspect ratio. If fill is false, the device will be drawn with the proper aspect ratio. When true, the device will be expanded to fill the screen. It
defaults to false.
boundary
This parameter specifies that the device outline and material interfaces
should be drawn. They will be drawn with the color specified by the
line.bound parameter. It defaults to off.
grid
The grid parameter specifies that the numerical grid the problem was
solved on should be drawn. The color will be with the color will be with
the line.grid parameter. It defaults to off.
axis
The axis parameter controls the drawing and labeling of axes around the
plot. If axis is true, the graph will be drawn with labeled axes. This parameter defaults true.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
95
PLOT.2D
line.grid
The line.grid parameter controls the line type or color that the axes and
grid will be drawn in. The parameter defaults to 1.
line.bound
This parameter specifies the line color to be used for the material boundaries. If boundary is not specified, this parameter is unimportant.
vornoi
This parameter specifies that the vornoi tessellation to be drawn.
diamonds
This option will cause the plot to draw small diamonds out at each point
location. Actually crosses are now plotted but the parameter name has not
yet been changed, just to confuse the opposition.
stress
This parameter plots the principal stresses throughout the structure. Vectors are drawn along the two principal axes of the stress tensor at each
point.
vleng
The length of the vectors is scaled so that the maximum stress has length
vleng, specified in microns.
line.com, line.ten
The sign of the stress is indicated by the color of the vectors drawn.
line.com is the color for compressive stress, line.ten is the color for tensile stress.
96
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PLOT.2D
vmax
If vmax is specified (in dynes/cm2), that stress will have length vleng, and
higher stresses will be omitted.
flow
Plots little arrows representing the velocity at each point. The vleng and
vmax parameters help out here too.
EXAMPLES
plot.2d grid
This command will draw the triangular grid and axes.
plot.2d bound x.min=2 x.max=5 clear=false
This command will draw the material interfaces and x axis between 2.0
and 5.0µm and will not clear the screen first.
plot.2d bound line.bound=2 diamonds y.max=5 axis=false
This command will draw the material interfaces with a maximum value of
y equal to 5.0µm. The boundaries will be drawn with line type 2, no axes,
and will draw the grid points.
BUGS
None
SEE ALSO
The contour and select statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
97
PRINT.1D
COMMAND
PRINT.1D
Print values along a one dimensional cross section.
SYNOPSIS
print.1d
[ ( x.value=<n> | y.value=<n> ) ]
[ silicon | oxide | nitride … ]
[ /exposed | /backside | /reflect | /silicon | /oxide |
/nitride … ]
[ arclength ] [ layers ] [ x.min=<n> ] [ x.max=<n> ]
[ format=<string> ]
DESCRIPTION
The print.1d command allows the user to print the values along cross sections through the device. It is also possible to integrate along a specified
line. The value printed is the value that has been selected, see select.
x.value, y.value
These parameters specify that the cross section is to be done at a constant
value as specified by the value of the parameter. x.value specifies a vertical cross section of the device, and y.value a horizontal slice. The parameter value is in microns. Only one of x.value or y.value can be specified for
a given device. In one dimensional mode, it is not necessary to specify a
position.
98
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PRINT.1D
silicon | oxide | nitride …
In addition to constant x or y cross sections, a one-dimensional print can
be specified along one side of an interface. The interface lies between material 1, named without an initial “/”, and material 2, named with a leading
“/”. For example, “print.1d oxide /silicon”. Thus “print.1d oxide /silicon”
will usually show something different from “print.1d silicon /oxide”. The
backside, reflecting or exposed surfaces of a material can be specified with
the appropriate parameter.
arclength
This parameter only has meaning for printing along the interface. The ordinate printed is the arc length along the boundary from the leftmost point
on the curve, in microns, if arclength is chosen. Otherwise the x value of
the interface location is printed. The leftmost point has ordinate equal to
its x coordinate in the mesh.
layers
This option instructs that the selected plot variable should integrated in
each material that is crossed. The integrated value and material width is
reported. Zero crossings of the variable are treated the same as material interfaces. This option imitates the SUPREM-III command, “print layers”,
and is probably most useful when doping is the selected variable.
x.min, x.max
These parameters allow the user to specify the limits of the print region.
Only values between these two will be displayed.
format
This allows the user to change the print format for the variable. It uses
standard C format expressions (e.g. 8.2f), minus the % sign. If the user is
unfamiliar with the C programming language, it might be best to not experiment.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
99
PRINT.1D
EXAMPLES
print.1d x.val=1.0 x.max=3.0
This command will print the selected value at x equal to 1µm between the
top of the mesh and the 3.0µm point.
print.1d y.val=0 layers
This will print the integrated value selected in each material layer crossed
by a horizontal slice at depth of 0.0.
print.1d sil /oxi
This will print the selected variable along the silicon side of the silicon oxide interface.
BUGS
If the interface between two materials comprises several disconnected
pieces, the end of one arc is joined incorrectly to the start of the next.
The interface between materials is usually ordered left-to-right, but it is
possible to confuse the routine and get right-to-left.
There is no way to specify a line at a fixed distance from an interface.
There is no simple way to follow the “upper” surface of a layer if it has
several different layers on top of it.
SEE ALSO
The select, plot.1d, and printf statements.
100
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PRINTF
COMMAND
PRINTF
A string printer and desk calculator.
SYNOPSIS
print [ string ]
DESCRIPTION
This command is similar to the echo command. The only difference is that
it splits its arguments up into white space separated pieces and passes each
piece separately to the real number parser. Both quotes and parenthesis
can be used to print spaces. This command is most useful in connection
with the movie parameter of the diffuse command.
EXAMPLES
printf jimmin at the jimjam frippin at the frotz
This will send the string
jimmin at the jimjam frippin at the frotz
to the standard output.
printf ( 15.0 - 12.0 * exp( 4.0 - 2.0 / 6.0 ) )
This will print the result of the arithmetic expression, which is of course,
8.373.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
101
PRINTF
printf ( 15.0 * exp ( -2.0 / (8.62e-5 * 1173.0) ) (12.0 * sqrt(2.0) )
This will print:
3.853e-8 16.97
printf "The Time is: " $time
Inside the movie parameter of the diffuse command, $time is a variable
that is set to the current time in the diffusion cycle. Consequently, if this is
used there, the command will print:
The Time is: 0.1
printf xfn(0.0, 0.0) yfn(0.0, 0.0) zfn(0.0, 0.0)
This will print the x location where y and z are both zero, the y location
where x and z are both zero, and the z location where x and y are both
zero.
BUGS
No known bugs.
SEE ALSO
The select statement for choosing z variables,
The section on conventions for a description of the real number parser,
The diffuse statement for examples of usage in the movie parameter.
102
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PROFILE
COMMAND
PROFILE
Read a one dimensional doping profile.
SYNOPSIS
profile
infile=<string>
( antimony | arsenic | boron | phosphorus | gallium |
interstitial | vacancy | beryllium | carbon |
germanium | selenium | isilicon | tin |
magnesium | zinc | generic )
DESCRIPTION
The profile allows the user to specify a file of one dimensional doping
data. This command allows the user to read data from another program,
e.g. SUPREM-III, or measured data. The new doping is added to any current doping that may exist. The file should have two columns of numbers,
depth and concentration. The file should have the depth in microns, and
the concentration in cm-3. Any lines which do contain two values are ignored as comments. A grid must be present for this command.
infile
The infile parameter selects the file name for data.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
103
PROFILE
antimony, arsenic, boron, phosphorus, intersticial, vacancy,
beryllium, magnesium, selenium, isilicon, tin, germanium,
zinc, carbon, generic
These parameters specify the type of impurity that forms the doping.
EXAMPLES
profile infile=foo phos
This command reads in a doping file named foo, containing a phosphorus
doping profile.
The file foo, for example, could look like:
#pulse doped buried phosphorus profile
0.2 1.0e5
0.21 1.0e19
0.30 1.0e19
0.31 1.0e5
Any area outside the specified doping layer is unchanged.
BUGS
There are no known bugs.
SEE ALSO
The initialize and structure statements.
104
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
REGION
COMMAND
REGION
Specify a mesh region.
SYNOPSIS
region
( silicon | oxide | nitride | poly | gas | oxynitr | photores |
aluminum | gaas )
xlo = <string> ylo = <string> xhi = <string> yhi = <string>
DESCRIPTION
This statement is used to specify the material of rectangles in a rectangular
mesh. Region statements should follow line statements. Every element
must be given some material, so at least one region statement is required
for each rectangular mesh.
silicon | oxide | nitride | poly | gas | oxynitr | photores |
aluminum | gaas
The material being specified.
xlo, ylo, xhi, yhi
The bounds of the rectangle being specified. The <string> value should be
one of the tags created in a preceding line statement.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
105
REGION
EXAMPLES
region silicon xlo=left xhi=right ylo=surf yhi=back
This line would make the entire mesh silicon (from the example on the
line page).
BUGS
None.
SEE ALSO
The line, boundary, and init statements.
106
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
SELECT
COMMAND
SELECT
Select the plot variable for the post-processing routines.
SYNOPSIS
select
[ z=<expr> ] [ label=<string> ] [ title=<string> ] [ temp=<n> ]
DESCRIPTION
The select statement is used to specify the variable for display in the contour statement, plot.1d statement, print.1d statement, and plot.2d statement. In short, all of the post-processing commands. No data will be
available for any of these statements unless this statement is specified first.
Only one variable can be selected at any one time and each select statement overrides any previous statements.
z
This parameter accepts a vector expression of several different vector variables for the z parameter. The operators *, /, +, -, ^ all work in the expected
way. The vector variables are listed below:
antimony
antimony concentration
arsenic
arsenic concentration
beryllium
beryllium concentration
boron
boron concentration
carbon
carbon concentration
cesium
cesium concentration
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
107
SELECT
ci.star
equilibrium interstitial concentration
cv.star
equilibrium vacancies concentration
doping
net active concentration
electrons
electron concentration
germanium
germanium
generic
generic impurity concentration
gold
gold concentration
interstitial
interstitial concentration
isilicon
silicon impurity concentration
magnesium
magnesium concentration
ni
intrinsic electron concentration
oxygen
oxygen concentration
phosphorus
phosphorus concentration
psi
potential
selenium
selenium concentration
Sxx, Sxy, Syy
components of stress in rectangular coordinates
tin
tin concentration
trap
unfilled interstitial trap concentration
vacancy
vacancy concentration
x
x coordinates
x.v
x velocity
y
y coordinates
y.v
y velocity
zinc
zinc concentration
Many of these are self explanatory. Potential is computed using charge
neutrality. The electron concentration is computed from the potential using
Boltzmann statistics.
108
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
SELECT
There also several function that are available for the user. These are:
abs
absolute value
active
active portion of the specified dopant
erf
error function
erfc
complimentary error function
exp
exponential
gradx
differentiates the argument with respect to x
grady
differentiates the argument with respect to y
log
logarithm
log10
logarithm base 10
scale
scales the value given by the maximum value
sqrt
square root
label
This is the string that appears on the y axis in a 1D plot. The default is the
select string.
title
This is the string printed in large letters across the top of the plot. Default
is the version number of the program.
temp
The temperature at which expressions are evaluated. It defaults to the last
temperature of diffusion.
EXAMPLES
select z=log10(arsen)
Choose as the plot variable the base 10 logarithm of the arsenic concentration.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
109
SELECT
select z=(phos - 5.0e14)
Choose as the plot variable the phosphorus concentration minus a constant
profile of 5.0×1014.
select z=(phos - 1.0e18 * exp ( y * y / 1.0e-8 ) )
Choose as the plot variable the difference between the phosphorus and an
analytic profile.
select z=(inter * vacan - ci.star * cv.star)
Choose the excess vacancy interstitial product as the plot variable.
BUGS
The version number needs to get updated more frequently.
SEE ALSO
All the other post-processing commands e.g plot.1d, plot.2d, print.1d,
contour, etc.
110
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
STRESS
COMMAND
STRESS
Calculate elastic stresses.
SYNOPSIS
stress [ temp1=<n> temp2=<n> ] [ nel=<n> ]
DESCRIPTION
The stress command allows the user to calculate stresses due to thin film
intrinsic stress or thermal mismatch.
temp1, temp2
These are the initial and final temperatures for calculating thermal mismatch stresses.
nel
This is the number of nodes per triangle to use. Currently only 6 or 7 are
allowed. 6 nodes is faster than 7 and usually gives adequate results, so 6 is
the default.
EXAMPLES
material nitride intrin.sig=1.4e10
stress
This calculates the stresses in the substrate and film arising from a nitride
layer which has an intrinsic stress of 1.4×1010 when deposited uniformly.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
111
STRESS
BUGS
The correct boundary conditions for a thermal mismatch problem are hard
to set up.
SEE ALSO
The material statement.
112
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
STRUCTURE
COMMAND
STRUCTURE
Read/write the mesh and solution information.
SYNOPSIS
structure
[ (infile=<string> | outfile=<string>) ]
[ pisces=<string> ] [ show ] [ backside.y=<n> ]
[ mirror ] [ left ] [ right ]
[ imagetool=<string> ]
[ x.min=<n> | x.max=<n> | y.min=<n> | y.max=<n> |
z.min=<n> | z.max=<n> | pixelx=<n> | pixely=<n> |
nxfac=<n> | nyfac=<n> | mode=<n> ]
[ simpl=<string> ] [ header=<string> ]
DESCRIPTION
The structure statement allows the user to read and write the entire mesh
and solution set. The data saved is from the current set of solution and impurity values.
infile, outfile
These parameters specify the name of the file to be read or written. An existing file will be overwritten.
pisces
This is how SUPREM-IV talks to PISCES. The file created is a pisces “geometry” file and is read with the “mesh infile=xxx geom” statement in PI-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
113
STRUCTURE
SCES (Sept. 87 version). Electrodes are generated at polysilicon and
aluminum interfaces with either silicon or oxide, and at the backside. The
electrode numbering is by SUPREM-IV region number, and is printed out.
Materials that PISCES does not recognize are stripped from the output
file. This includes polysilicon and aluminum layers.
show
The numbering of electrodes is displayed by plotting the structure and labeling each electrode node with its electrode number.
backside.y
Used in conjunction with the pisces parameter, the substrate (assumed to
be silicon) will be etched from the location specified by the argument to
backside.y to the bottom of the wafer. A backside contact extending across
the substrate in the x-direction will be placed at this y-value.
mirror left
mirror right
Mirrors the grid around its left or right boundary. Useful for turning half-aMOSFET simulations into PISCES grids. The default is to reflect around
the right axis.
imagetool
This string parameter specifies the name of the binary raster file that can
be used by NCSA programs such as XImage. The entire structure will be
plotted unless clipped by the window parameters x.min, x.max, y.min, and
y.max. In addition the size of the raster image is controlled by the parameters pixelx and pixely. Z values are derived using the select command. All
z values will be plotted unless clipped with z.min and z.max. For details
on the parameters associated with imagetool files, see below.
114
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
STRUCTURE
x.min
This float parameter is minimum x-value in microns used in generating the
raster image. x.min defaults to the left edge of the entire structure.
x.max
This float parameter is maximum x-value in microns used in generating
the raster image. x.max defaults to the right edge of the entire structure.
y.min
This float parameter is minimum y-value in microns used in generating the
raster image. y.min defaults to the top edge of the entire structure.
y.max
This float parameter is maximum y-value in microns used in generating
the raster image. y.max defaults to the bottom edge of the entire structure.
z.min
This float parameter is the minimum z-value used for generating the raster
image. The z array is created using the select command. If the actual z-value is less than z.min, the value will be given the same color as z.min.
z.max
This float parameter is the maximum z-value used for generating the raster
image. The z array is created using the select command. If the actual z-value is greater than z.max, the value will be given the same color as z.max.
pixelx
This integer parameter is the number of pixels in the x-direction for the
raster image. The default value is 400 pixels.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
115
STRUCTURE
pixely
This integer parameter is the number of pixels in the y-direction for the
raster image. The default value is 200 pixels.
nxfac
This integer parameter is the amount of linear interpolation in the x-direction to be done on the rectangular grid that will be used to create the raster
image. The default value of 1 gives the most resolution at the cost of higher CPU usage. A higher value will give a slightly coarser picture but will
take less CPU time.
nyfac
This integer parameter is the amount of linear interpolation in the y-direction to be done on the rectangular grid that will be used to create the raster
image. The default value of 1 gives the most resolution at the cost of higher CPU usage. A higher value will give a slightly coarser picture but will
take less CPU time.
mode
This integer parameter is a special flag (0 or 1) useful for plotting doping
concentrations. It assumes that the follow select statement was issued:
select z=sign(bor-phos-ars)*log10(abs(bor-phos-ars))
The colors are then mapped between -14 and 14. This compresses the color spectrum to allow more colors in the region of interest.
clear
This integer parameter clears a global counter which counts frame numbers is association with the movie parameter of the diffuse command.
116
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
STRUCTURE
count
This integer parameter increments the global counter. When used with the
movie parameter of the diffuse command, a sequence of image files can
be generated whose last 3 characters are numbers. Files in this type of sequence can be easily animated using NCSA XImage.
simpl
This string parameter generates a file in the SIMPL-2 format. This is necessary to incorporate SUPREM-IV information into the SIMPL-IPX system. Another parameter, header, must also be specified.
header
This string parameter is the name of the file used to describe the cross section to be described. This is the first few lines from a SIMPL-2 file. Usually these files are automatically generated when using SUPREM-IV within
the SIMPL-IPX environment.
EXAMPLES
structure infile=foo
This command reads in a previously saved structure in file foo.
structure pisces=baz show backside.y=5.0
Writes a PISCES-II compatible file. The locations and number of the electrodes will be displayed. In addition the silicon substrate will be removed
for y > 5.0 and a backside contact will be placed at y = 5.0.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
117
STRUCTURE
structure imagetool=foo x.min=-1.0 x.max=1.0
y.min=-1.0 y.max=1.0 pixelx=300 pixely=150
Writes an binary raster file for XImage of size 300 by 150 pixels. Only
data in the window -1.0µm ≤ x ≤ 1.0µm, -1.0µm ≤ y ≤ 1.0µm is shown in
the image.
structure simpl=foo.cross header=headerfile
Writes a SIMPL-2 ASCII file using cross section information from file
headerfile.
BUGS
The show option echoes a lot of nonsense while drawing the structure.
Beware of rounding errors when mirroring. If the left or right boundary is
not smooth to within 0.1Å, some points will be duplicated.
SEE ALSO
The initialize statement.
118
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Models
DESCRIPTION
This section contains the commands used to change model parameters and
coefficients. The parameters and equations they belong to are described
briefly on the statement descriptions. References are provided, where necessary, to help clarify the physics involved in the simulator.
The file for the initialization of all the constants is human readable (usually called modelrc). Unfortunately, this means that SUPREM-IV.GS can be
slow in starting up because it has to parse the file. Local modification of
the file is encouraged, because many of the parameters are areas of active
research and can not be guaranteed, other parameters may be dependent
upon the equipment used locally.
The model statements can be broken up by diffusion impurity. All the parameters concerning arsenic diffusion, segregation, and clustering are on
the same statement. The oxide statement contains some material information as well as parameters for oxidant diffusion.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
119
Models
BUGS
These commands implement the best physics we have worked out to date.
However, that is a day to day proposition.
SEE ALSO
See the other model statement descriptions for more detail. Most of the
model statements will include references to the relevant published papers.
Please see these Stanford University Ph.D. theses for more information.
Paul Fahey – Defect Models, Fractional Interstitialcy,
Peter Griffin – Defect Models and Diffusion, Experiments,
Mark Law – Defect Models and Diffusion, Numerical Techniques,
Paul Packan – Oxidation Enhanced Diffusion Experiments,
Conor Rafferty – Oxidation Models and Stress.
Heyward Robinson – Defect Models and Diffusion.
Emily Allen – Defect Models and Diffusion.
Jeff Murray – Defect Models and Diffusion.
Chris Pass– Defect Models and Diffusion.
Linda Vanasupa – Defect Models and Activation.
M. D. Deal – Defect Models and Diffusion.
120
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ANTIMONY
COMMAND
ANTIMONY
Set the coefficients of antimony kinetics.
SYNOPSIS
antimony
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas |
/poly | /gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of antimony diffusion and segregation. The diffusion equation for antimony is [1,2]:
∂C T
∂t
= ∇ DV CT
CV
*
CV
CV n
CI
CI n
∇ln C T *  + D I C T * ∇ln C T * 
 CV ni 
 CI ni 
CI
(EQ 3)
where CT is the total chemical concentration of antimony, CV and CI are
the vacancy and interstitial concentrations, the superscript * refers to the
equilibrium concentration, DV and DI are the diffusivities with vacancies
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
121
ANTIMONY
and interstitials, and n and ni refer to the electron concentration and the intrinsic concentration respectively. The diffusivities are given by:
DV = ( 1 − Fi ) ( DX + DM
DI = Fi ( DX + DM
n
)
ni
n
)
ni
(EQ 4)
(EQ 5)
DX and DM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 6)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the antimony
diffusing with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. Dix.0 defaults to 0.214 cm2/sec in silicon,
and Dix.E defaults to 3.65 eV in silicon [3]. DX is calculated using a standard Arrhenius relationship.
122
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ANTIMONY
Dim.0, Dim.E
These floating point parameters allow the specification of the antimony
diffusing with singly negative defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to 15.0 cm2/sec in
silicon, and Dim.E defaults to 4.08 eV in silicon [3]. DM is calculated using
a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether antimony diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.05 [4].
implanted, grown.in
Specifies whether the Dix, Dim, or Fi coefficients apply to implanted or
grown-in antimony. If neither is specified then a specified parameter applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are [5]:
ss.temp
ss.conc
800˚C
2.3×1019 cm-3
900˚C
3.0×1019 cm-3
1000˚C
4.0×1019 cm-3
1100˚C
4.8×1019 cm-3
1200˚C
6.2×1019 cm-3
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
123
ANTIMONY
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default antimony is a donor.
EXAMPLES
antimony silicon Dix.0=0.214 Dix.E=3.65
This command changes the neutral defect diffusivity in silicon.
antimony silicon /oxide Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the silicon – silicon dioxide interface. The silicon concentration will be 30.0 times the oxide concentration in equilibrium.
124
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ANTIMONY
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
2. D. Mathiot and J.C. Pfister, “Dopant Diffusion in Silicon: A consistent
view involving nonequilibrium defects,” J. Appl. Phys., 55(10), p.
3518, 1984.
3. R.B. Fair, “Concentration Profiles of Diffused Dopants in Silicon,” Impurity Doping Processes in Silicon, Yang ed., 1981, North-Holland,
New York.
4. P. Fahey, G. Barbuscia, M. Moslehi and R.W. Dutton, “Kinetics of
Thermal Nitridation Processes in the Study of Dopant Diffusion Mechanisms in Silicon,” Appl. Phys. Lett., 46(8), p. 784, 1985.
5. F.A. Trumbore, “Solid Solubilities of Impurity Elements in Germanium
and Silicon,” Bell System Tech Journal, 1960.
SEE ALSO
The arsenic, boron, phosphorus, interstitial, and vacancy statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
125
ARSENIC
COMMAND
ARSENIC
Set the coefficients of arsenic kinetics.
SYNOPSIS
arsenic
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ Ctn.0=<n> ] [ Ctn.E=<n> ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of arsenic
diffusion and segregation. The diffusion equation for arsenic is [1,2]:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV n
CI
CI n
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 7)
where CT and CA are the total chemical and active concentrations of arsenic, CV and CI are the vacancy and interstitial concentrations, the superscript * refers to the equilibrium concentration, DV and DI are the
126
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ARSENIC
diffusivities with vacancies and interstitials, and n and ni refer to the electron concentration and the intrinsic concentration respectively. The diffusivities are given by:
DV = ( 1 − Fi ) ( DX + DM
DI = Fi ( DX + DM
n
)
ni
n
)
ni
(EQ 8)
(EQ 9)
DX and DM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 10)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the arsenic diffusing with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. Dix.0 defaults to 0.214 cm2/sec in silicon,
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
127
ARSENIC
and Dix.E defaults to 3.65 eV in silicon [3]. DX is calculated using a standard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the arsenic diffusing with singly negative defects. Dim.0 is the pre-exponential constant
and Dim.E is the activation energy. Dim.0 defaults to 15.0 cm2/sec in silicon, and Dim.E defaults to 4.08 eV in silicon [3]. DM is calculated using a
standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether arsenic diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.20 [4].
implanted, grown.in
Specifies whether the Dix, Dim, or Fi coefficients apply to implanted or
grown-in arsenic. If neither is specified then a specified parameter applies
to both.
Ctn.0, Ctn.E
These parameters specify the clustering coefficients for arsenic. The parameters are respectively the pre-exponential coefficient and the activation
energy. The total cluster coefficient obeys a standard Arrhenius relationship. The active concentration, CA is calculated using:
C T = C A 1 + C tn (
n 2 CV
)
ni C*
(EQ 11)
V
Physically, this represents clustering of arsenic with doubly negative vacancies. The default parameters for Ctn.0 and Ctn.E in silicon are
5.9×10-24 and 0.60 eV, respectively[3].
128
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ARSENIC
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are [5]:
ss.temp
ss.conc
800˚C
1.60×1020 cm-3
900˚C
1.63×1020 cm-3
1000˚C
2.14×1020 cm-3
1100˚C
5.00×1020 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default arsenic is a donor.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
129
ARSENIC
EXAMPLES
arsenic silicon Dix.0=8.0 Dix.E=3.65
This command changes the neutral defect diffusivity in silicon.
arsenic silicon /oxide Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the silicon – silicon dioxide interface. The silicon concentration will be 30.0 times the oxide concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
2.
3.
4.
5.
130
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
D. Mathiot and J.C. Pfister, “Dopant Diffusion in Silicon: A consistent
view involving nonequilibrium defects,” J. Appl. Phys., 55(10), p.
3518, 1984.
R.B. Fair, “Concentration Profiles of Diffused Dopants in Silicon,” Impurity Doping Processes in Silicon, Yang ed., 1981, North-Holland,
New York.
P. Fahey, G. Barbuscia, M. Moslehi and R.W. Dutton, “Kinetics of
Thermal Nitridation Processes in the Study of Dopant Diffusion Mechanisms in Silicon,” Appl. Phys. Lett., 46(8), p. 784, 1985.
D. Nobili, A. Carabelas, G. Celotti, and S. Solmi, Journal of the Electrochemical Society, 130, p 922, 1983.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ARSENIC
SEE ALSO
The antimony, boron, phosphorus, interstitial, and vacancy statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
131
BERYLLIUM
COMMAND
BERYLLIUM
Set the coefficients of beryllium kinetics.
SYNOPSIS
beryllium
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dip.0=<n> ] [ Dip.E=<n> ] [ Dipp.0=<n> ] [ Dipp.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of beryllium diffusion and segregation. The diffusion equation for beryllium is:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV p
CI
CI p
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 12)
where CT and CA are the total chemical and active concentrations of beryllium, CA is the total electrically active concentration of beryllium, CV
and CI are the vacancy and interstitial concentrations, the superscript * re-
132
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BERYLLIUM
fers to the equilibrium value, DV and DI are the diffusivities with vacancies and interstitials, and p and ni refer to the hole concentration and the
intrinsic electron concentration respectively. The diffusivities are given
by:
p
p 2

D V = ( 1 − F i ) D X + D p ( ) + D PP ( )

ni
ni 
(EQ 13)
p
p 2

D I = F i D X + D p ( ) + D PP ( )

ni
ni 
(EQ 14)
DX , DP , and DPP are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 15)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
133
BERYLLIUM
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the beryllium diffusivity with neutral defects. Dix.0 is the pre-exponential constant
and Dix.E is the activation energy. Dix.0 defaults to 0.0 cm2/sec in gallium
arsenide, and Dix.E defaults to 0.0 eV in gallium arsenide. DX is calculated
using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP , the beryllium diffusivity with singly positive defects. Dip.0 is the pre-exponential
constant and Dip.E is the activation energy. Dip.0 defaults to 2.1×10-6 cm2/
sec for implanted beryllium in gallium arsenide and 2.1×10-6 cm2/sec for
grown-in beryllium in gallium arsenide, and Dip.E defaults to 1.74 eV for
both in gallium arsenide [1, 2, 3]. DP is calculated using a standard Arrhenius relationship.
Dipp.0, Dipp.E
These floating point parameters allow the specification of DPP , the beryllium diffusivity with doubly positive defects. Dipp.0 is the pre-exponential
constant and Dipp.E is the activation energy. Dipp.0 defaults to 0.0 cm2/
sec in gallium arsenide, and Dipp.E defaults to 0.0 eV in gallium arsenide.
DPP is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether beryllium diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 1.0.
implanted, grown.in
Specifies whether the Dix, Dip, Dipp, or Fi coefficients apply to implanted
or grown-in beryllium. If neither is specified then a specified parameter
applies to both.
134
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BERYLLIUM
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are:
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, beryllium is an acceptor.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
135
BERYLLIUM
EXAMPLES
beryllium gaas implanted Dip.0=2.2e-6 Dip.E=1.76
This command changes the positive defect diffusivity for implanted beryllium in gallium arsenide.
beryllium gaas /nitride Seg.0=1126.0 Seg.E=0.91
Trn.0=1.66e-7
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be half the nitride concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. M.D. Deal and H.G. Robinson, “Diffusion of Implanted Beryllium in P
and N Type GaAs,” Appl. Phys. Lett. 55, 1990.
136
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BERYLLIUM
SEE ALSO
The antimony, arsenic, boron, carbon, generic, germanium, interstitial, magnesium, phosphorus, selenium, isilicon, tin, vacancy, and
zinc statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
137
BORON
COMMAND
BORON
Set the coefficients of boron kinetics.
SYNOPSIS
boron
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dip.0=<n> ] [ Dip.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of boron
diffusion and segregation. The diffusion equation for boron is [1,2]:
∂C T
∂t
= ∇ DV CA
CV
C
C
C
 C V p  + D C I ∇ln C I p 
∇ln
A
I
A
A
*
*
 C *V n i 
 C *I n i 
CV
CI
(EQ 16)
where CT and CA are the total chemical and active concentrations of boron, CA is the total electrically active concentration of boron, CV and CI
are the vacancy and interstitial concentrations, the superscript * refers to
138
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BORON
the equilibrium value, DV and DI are the diffusivities with vacancies and
interstitials, and p and ni refer to the hole concentration and the intrinsic
electron concentration respectively. The diffusivities are given by:
DV = ( 1 − Fi ) ( DX + DP
DI = Fi ( DX + DP
p
)
ni
p
)
ni
(EQ 17)
(EQ 18)
DX and DP are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 19)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the boron
diffusivity with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. Dix.0 defaults to 0.28 cm2/sec in silicon,
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
139
BORON
and Dix.E defaults to 3.46 eV in silicon [3]. DX is calculated using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP , the boron
diffusivity with singly positive defects. Dip.0 is the pre-exponential constant and Dip.E is the activation energy. Dip.0 defaults to 0.23 cm2/sec in
silicon, and Dip.E defaults to 3.46 eV in silicon [3]. DP is calculated using
a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether boron diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.8 [4].
implanted, grown.in
Specifies whether the Dix, Dip, or Fi coefficients apply to implanted or
grown-in boron. If neither is specified then a specified parameter applies
to both.
ss.clear
This parameter clears the currently stored solid solubility data.
140
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BORON
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are [5].
ss.temp
ss.conc
ss.temp
ss.conc
800˚C
-3
3.45×10 cm
1050˚C
1.53×1020 cm-3
825˚C
4.13×1019 cm-3
1075˚C
1.73×1020 cm-3
850˚C
4.90×1019 cm-3
1100˚C
1.94×1020 cm-3
875˚C
5.78×1019 cm-3
1125˚C
2.16×1020 cm-3
900˚C
6.76×1019 cm-3
1150˚C
2.40×1020 cm-3
925˚C
7.86×1019 cm-3
1175˚C
2.66×1020 cm-3
950˚C
9.08×1019 cm-3
1200˚C
2.94×1020 cm-3
975˚C
1.04×1020 cm-3
1225˚C
3.24×1020 cm-3
1000˚C
1.19×1020 cm-3
1250˚C
3.55×1020 cm-3
1025˚C
1.35×1020 cm-3
1275˚C
3.89×1020 cm-3
19
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
141
BORON
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default boron is an acceptor.
EXAMPLES
boron silicon Dix.0=0.28 Dix.E=3.46
This command changes the neutral defect diffusivity in silicon.
boron silicon /oxide Seg.0=1126.0 Seg.E=0.91 Trn.0=1.66e-7
This command will change the segregation parameters at the silicon – silicon dioxide interface. The silicon concentration will be half the oxide concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
2. D. Mathiot and J.C. Pfister, “Dopant Diffusion in Silicon: A consistent
view involving nonequilibrium defects,” J. Appl. Phys., 55(10), p.
3518, 1984.
3. G.P. Barbuscia, G. Chin, R.W. Dutton, T. Alvarez and L. Arledge,
“Modeling of Polysilicon Dopant Diffusion for Shallow Junction Bipo-
142
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
BORON
lar Technology,” International Electron Devices Meeting, San Francisco, p. 757, 1984.
4. P.A. Packan and J.D. Plummer, “Temperature and Time Dependence of
B and P Diffusion in Si During Surface Oxidation,” J. Appl. Phys.,
68(8), 1990.
5. A. Armigliato, D. Nobili, P. Ostoja, M. Servidori and S. Solmi, “Solubility and Precipitation of Boron in Silicon and Supersaturation Resulting by Thermal Predeposition,” Journal of Applied Physics.
SEE ALSO
The antimony, arsenic, interstitial, phosphorus, and vacancy statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
143
CARBON
COMMAND
CARBON
Set the coefficients of carbon kinetics.
SYNOPSIS
carbon
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dip.0=<n> ] [ Dip.E=<n> ] [ Dipp.0=<n> ] [ Dipp.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of carbon
diffusion and segregation. The diffusion equation for carbon is:
∂C T
∂t
= ∇ DV CA
CV
C
C
C
 C V p  + D C I ∇ln C I p 
∇ln
A
I
A
A
*
*
 C *V n i 
 C *I n i 
CV
CI
(EQ 20)
where CT and CA are the total chemical and active concentrations of carbon, CA is the total electrically active concentration of carbon, CV and CI
are the vacancy and interstitial concentrations, the superscript * refers to
144
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
CARBON
the equilibrium value, DV and DI are the diffusivities with vacancies and
interstitials, and p and ni refer to the hole concentration and the intrinsic
electron concentration respectively. The diffusivities are given by:
p
p 2

D V = ( 1 − F i ) D X + D p ( ) + D PP ( )

ni
ni 
p
p 2

D I = F i D X + D p ( ) + D PP ( )

ni
ni 
(EQ 21)
(EQ 22)
DX , DP , and DPP are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 23)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the carbon
diffusivity with neutral defects. Dix.0 is the pre-exponential constant and
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
145
CARBON
Dix.E is the activation energy. Dix.0 defaults to 1.0×10-16 cm2/sec in galli-
um arsenide, and Dix.E defaults to 0.0 eV in gallium arsenide [1, 2]. DX is
calculated using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP, the carbon
diffusivity with singly positive defects. Dip.0 is the pre-exponential constant and Dip.E is the activation energy. Dip.0 defaults to 0.0 cm2/sec in
gallium arsenide and Dip.E defaults to 0.0 eV in gallium arsenide. DP is
calculated using a standard Arrhenius relationship.
Dipp.0, Dipp.E
These floating point parameters allow the specification of DPP, the carbon
diffusivity with doubly positive defects. Dipp.0 is the pre-exponential constant and Dipp.E is the activation energy. Dipp.0 defaults to 0.0 cm2/sec in
gallium arsenide, and Dipp.E defaults to 0.0 eV in gallium arsenide. DPP
is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether carbon diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 1.0.
implanted, grown.in
Specifies whether the Dix, Dip, Dipp, or Fi coefficients apply to implanted
or grown-in carbon. If neither is specified then a specified parameter applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
146
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
CARBON
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are:
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, carbon is an acceptor.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
147
CARBON
EXAMPLES
carbon gaas implanted Dip.0=2.2e-6 Dip.E=1.76
This command changes the positive defect diffusivity for implanted carbon in gallium arsenide.
carbon gaas /nitride Seg.0=1126.0 Seg.E=0.91 Trn.0=1.66e-7
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be half the nitride concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
SEE ALSO
The antimony, arsenic, beryllium, boron, generic, germanium, interstitial, magnesium, phosphorus, selenium, isilicon, tin, vacancy, and
zinc statements.
148
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
GENERIC
COMMAND
GENERIC
Set the coefficients for a generic impurity’s kinetics.
SYNOPSIS
generic
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ]
[ Dimmm.0=<n> ] [ Dimmm.E=<n> ]
[ Dip.0=<n> ] [ Dip.E=<n> ]
[ Dipp.0=<n> ] [ Dipp.E=<n> ]
[ Dippp.0=<n> ] [ Dippp.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly | gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of a generic impurity’s diffusion and segregation. The diffusion equation for the generic impurity is:
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
149
GENERIC
∂C T
∂t
= ∇ DV CA
CV
C
C
C
 C V p  + D C I ∇ln C I p 
∇ln
A
I
A
A
*
*
 C *V n i 
 C *I n i 
CV
CI
(EQ 24)
where CT and CA are the total chemical and electrically active concentrations of the generic impurity, CV and CI are the vacancy and interstitial
concentrations, the superscript * refers to the equilibrium value, DV and DI
are the diffusivities with vacancies and interstitials, and p and ni refer to
the hole concentration and the intrinsic electron concentration respectively. The diffusivities are given by:
DV = ( 1 − Fi )
DI = Fi
DX + DM (
n
n 2
n
) + D MM ( ) + D MMM ( )
ni
ni
ni
p
p 2
p
+ D p ( ) + D PP ( ) + D PPP ( )
ni
ni
ni
DX + DM (
n
n 2
n
) + D MM ( ) + D MMM ( )
ni
ni
ni
p
p 2
p
+ D p ( ) + D PP ( ) + D PPP ( )
ni
ni
ni
3
(EQ 25)
3
3
(EQ 26)
3
DX , DM , DMM , DMMM , DP , DPP,and DPPP are described in greater detail
below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
150
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
(EQ 27)
GENERIC
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the generic
impurity’s diffusivity with neutral defects. Dix.0 is the pre-exponential
constant and Dix.E is the activation energy. Dix.0 defaults to 0.0 cm2/sec
and Dix.E defaults to 0.0 eV. DX is calculated using a standard Arrhenius
relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of DM , the generic
impurity’s diffusivity with singly positive defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to
0.0 cm2/sec and Dim.E defaults to 0.0 eV. DM is calculated using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of DMM , the generic impurity’s diffusivity with doubly positive defects. Dimm.0 is the preexponential constant and Dimm.E is the activation energy. Dimm.0 defaults to 0.0 cm2/sec and Dimm.E defaults to 0.0 eV. DMM is calculated using a standard Arrhenius relationship.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
151
GENERIC
Dimmm.0, Dimmm.E
These floating point parameters allow the specification of DMMM , the generic impurity’s diffusivity with triply positive defects. Dimmm.0 is the
pre-exponential constant and Dimmm.E is the activation energy.
Dimmm.0 defaults to 0.0 cm2/sec and Dimmm.E defaults to 0.0 eV. DMMM
is calculated using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP, the generic
impurity’s diffusivity with singly positive defects. Dip.0 is the pre-exponential constant and Dip.E is the activation energy. Dip.0 defaults to
0.0 cm2/sec and Dip.E defaults to 0.0 eV. DP is calculated using a standard
Arrhenius relationship.
Dipp.0, Dipp.E
These floating point parameters allow the specification of DPP , the generic
impurity’s diffusivity with doubly positive defects. Dipp.0 is the pre-exponential constant and Dipp.E is the activation energy. Dipp.0 defaults to
0.0 cm2/sec and Dipp.E defaults to 0.0 eV. DPP is calculated using a standard Arrhenius relationship.
Dippp.0, Dippp.E
These floating point parameters allow the specification of DPPP , the generic impurity’s diffusivity with triply positive defects. Dippp.0 is the pre-exponential constant and Dippp.E is the activation energy. Dippp.0 defaults
to 0.0 cm2/sec and Dippp.E defaults to 0.0 eV. DPPP is calculated using a
standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether generic diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.0.
152
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
GENERIC
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, Dimmm, Dip, Dipp, Dippp, or Fi
coefficients apply to implanted or grown-in generic. If neither is specified
then a specified parameter applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are:
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
153
GENERIC
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. There is no default set so the type must be
set before using the generic impurity.
EXAMPLES
generic gaas implanted Dip.0=2.2e-6 Dip.E=1.76
This command changes the positive defect diffusivity for an implanted generic impurity in gallium arsenide.
generic gaas /nitride Seg.0=1126.0 Seg.E=0.91 Trn.0=1.66e-7
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be half the nitride concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, germanium, interstitial, magnesium, phosphorus, selenium, isilicon, tin, vacancy, and
zinc statements.
154
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
GERMANIUM
COMMAND
GERMANIUM
Set the coefficients of germanium kinetics.
SYNOPSIS
germanium
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ] [ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of germanium diffusion and segregation. The diffusion equation for germanium is:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV n
CI
CI n
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 28)
where CT and CA are the total chemical and active concentrations of germanium, CV and CI are the vacancy and interstitial concentrations, the superscript * refers to the equilibrium concentration, DV and DI are the
diffusivities with vacancies and interstitials, and n and ni refer to the elec-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
155
GERMANIUM
tron concentration and the intrinsic concentration respectively. The diffusivities are given by:
n
n 2

D V = ( 1 − F i ) D X + D M ( ) + D MM ( )

ni
ni 
(EQ 29)
n
n 2

D I = F i D X + D M ( ) + D MM ( )

ni
ni 
(EQ 30)
DX , DM , and DMM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 31)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the germanium
diffusing with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. Dix.0 defaults to 0.0 cm2/sec in gallium ars-
156
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
GERMANIUM
enide, and Dix.E defaults to 0.0 eV in gallium arsenide. DX is calculated
using a standard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the germanium
diffusing with singly negative defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to 0.0 cm2/sec in
gallium arsenide, and Dim.E defaults to 0.0 eV in gallium arsenide. DM is
calculated using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of the germanium
diffusing with doubly negative defects. Dimm.0 is the pre-exponential
constant and Dimm.E is the activation energy. Dimm.0 defaults to
1.1×10-3 cm2/sec in gallium arsenide, and Dimm.E defaults to 2.9 eV in
gallium arsenide [1,2]. DMM is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether germanium diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.0.
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, or Fi coefficients apply to implanted or grown-in germanium. If neither is specified then a specified parameter applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
157
GERMANIUM
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, germanium is an donor.
EXAMPLES
germanium gaas implanted Dimm.0=2.1e-3 Dimm.E=3.1
This command changes the doubly negative defect diffusivity for implanted germanium in silicon.
158
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
GERMANIUM
germanium gaas /nitride Seg.0=30.0 Trn.0=1.66e-7
Seg.E=0.0
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be 30.0 times the nitride concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. E.L. Allen, J.J. Murray, M.D. Deal, J.D. Plummer, K.S.Jones, and W.S.
Robert, “Diffusion of Ion-Implanted Group IV Dopants in GaAs,” J.
Electrochem. Soc., 138, p. 3440, 1991.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, interstitial,
magnesium, phosphorus, selenium, isilicon, tin, vacancy, and zinc
statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
159
INTERSTITIAL
COMMAND
INTERSTITIAL
Set coefficients of interstitial kinetics.
SYNOPSIS
interstitial
( silicon | oxide | poly | oxynitr | nitride | gas | gaas )
[ D.0=<n> ] [ D.E=<n> ]
[ Kr.0=<n> ] [ Kr.E=<n> ]
[ Cstar.0=<n> ] [ Cstar.E=<n> ]
[ ktrap.0=<n> ] [ ktrap.E=<n> ]
[ neu.0=<n> ] [ neu.E=<n> ] [ neg.0=<n> ] [ neg.E=<n> ]
[ dneg.0=<n> ] [ dneg.E=<n> ] [ tneg.0=<n> ] [ tneg.E=<n>]
[ pos.0=<n> ] [ pos.E=<n> ] [ dpos.0=<n> ] [ dpos.E=<n> ]
[ tpos.0=<n> ] [ tpos.E=<n> ]
[ ( /silicon | /oxide | /poly | /oxynitr | /nitride | /gas |
/gaas ) ]
[ time.inj ] [ growth.inj ] [ recomb ] [ segregation ]
[ Ksurf.0=<n> ] [ Ksurf.E=<n> ]
[ Krat.0=<n> ] [ Krat.E=<n> ]
[ Kpow.0=<n> ] [ Kpow.E=<n> ]
[ vmole=<n> ] [ theta.0=<n> ] [ theta.E=<n> ]
[ Gpow.0=<n> ] [ Gpow.E=<n> ]
[ A.0=<n> ] [ A.E=<n> ] [ t0.0=<n> ] [ t0.E=<n> ]
[ Tpow.0=<n> ] [ Tpow.E=<n> ]
[ rec.str=<s> ] [ inj.str=<s> ]
[ Seg.E=<n> ] [ Seg.0=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
160
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INTERSTITIAL
DESCRIPTION
This statement allows the user to specify values for coefficients of interstitial continuity equation. The statement allows coefficients to be specified
for each of the materials. Of course, the meaning of a lattice interstitial in
an amorphous region is a philosophical topic. SUPREM-IV has default
values only for silicon, gallium arsenide, and the interfaces with silicon.
Polysilicon has not been characterized as extensively, and its parameters
default to those for silicon.
The interstitials obey a complex diffusion equation which can be written
[1]:
∑
∂ ( C I − C ET ) = ∇ ( − J −
J AI ) − R
I
∂t
imp
(EQ 32)
where CI is the interstitial concentration, CET is the number of empty interstitial traps, JI refers to the interstitial flux, JAI refers to the flux of impurity A diffusing with interstitials, and R is all sources of bulk
recombination of interstitials. In the two.dim model (see method) the fluxes from the dopants, JAI , are ignored. Only in the full.cpl model are they
computed and included in the interstitial equation. This model represents
the diffusion of all interstitials, paired or unpaired, and can be derived
from assuming thermal equilibrium between the species and that the simple pairing reactions are dominant [1].
The trap reaction was described by Griffin [2]. This model explains some
of the wide variety of diffusion coefficients extracted from several different experimental conditions. The trap equation is:
∂C ET = − K C C − e C * ( C − C )
T
ET I
I
T
ET
1 − e*
∂t
*
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
(EQ 33)
161
INTERSTITIAL
where CT is the total trap concentration, KT is the trap reaction coefficient,
e* is the equilibrium trap occupancy ratio. (see trap for a more complete
discussion). Instead of the reaction, the time derivative is used in the interstitial equation because it has better properties in the numerical calculation.
The pair fluxes are the interstitial portions of the flux as described in each
of the models for the impurities. (see antimony, arsenic, boron, and phosphorus) The interstitial flux can be written [1]:
*
−JI = DI CI ∇
CI
(EQ 34)
*
CI
It is important to note that the equilibrium concentration, C*I is a function
of Fermi level [3]. This flux accounts correctly for the effect of an electric
field on the charged portion of the defect concentration. The bulk recombination is simple interaction between interstitials and vacancies. This can
be expressed:
*
*
R = KR ( CI CV − CI CV)
(EQ 35)
where KR is the bulk recombination coefficient, and CV and CV* are the
vacancy and vacancy equilibrium concentration, respectively.
The defects obey a flux balance boundary condition, as described by Hu
[4]:
J I n + K I ( C I − C *I ) = g
(EQ 36)
where n is the surface normal, KI is the surface recombination constant,
and g is the generation, if any, at the surface. This expression has been
used with success on several different surface types.
162
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INTERSTITIAL
silicon, oxide, poly, oxynitr, nitride, gaas, gas
These parameters allow the specification of the material for which the parameters apply.
D.0, D.E
These floating point parameters are used to specify the diffusion coefficient of the interstitials. The units are in cm2/sec. The default values are
1×106 cm2/sec and 3.22 eV [5] for Si and 1×10-12 cm2/sec and 0.0 eV for
GaAs.
Kr.0, Kr.E
These floating point parameters allow the specification of the bulk recombination rate in cm3/sec. The default is 1.4 cm3/sec and 3.99 eV [6] for Si
and 1×1014 cm3/sec and 0.0 eV for GaAs.
Cstar.0, Cstar.E
These parameters allow the specification of the total equilibrium concentration of interstitials in intrinsically doped conditions. The default values
are 3.1×1019 cm-3 and 1.58 eV [5] for Si and 1×1014 cm-3 and 0.0 eV for
GaAs.
ktrap.0, ktrap.E
These values allow the specification of the trap reaction rate. At present, it
is very difficult to extract exact values for these parameters. The default
values assume that the trap reaction is limited by the interstitial concentration. A diffusion limited model has been assumed [6] and results in defaults of 1.1×10-2 cm3/sec and 3.22 eV for Si, the same values are used for
GaAs.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
163
INTERSTITIAL
neu.0, neu.E, neg.0, neg.E, dneg.0, dneg.E, tneg.0, tneg.E,
pos.0, pos.E, dpos.0, dpos.E, tpos.0, tpos.E
These values allow the user to specify the relative concentration of interstitials in the various charge states (neutral, negative, double negative, triple negative, positive, double positive, and triple positive) under intrinsic
doping conditions. For example, in intrinsic conditions, the concentration
of doubly negative interstitials is given by:
C Star dneg
=
CI =
(EQ 37)
neu + neg + dneg + tneg + pos + dpos + tpos
where CStar is the total equilibrium concentration in intrinsic doping conditions. In extrinsic conditions, the total equilibrium concentration is given
by [3]:
2
neu + neg
*
C I = C Star
3
2
n
n
n
p
p
p
+ dneg ( ) + tneg ( ) + pos + dpos ( ) + tpos ( )
ni
ni
ni
ni
ni
ni
neu + neg + dneg + tneg + pos + dpos + tpos
3
(EQ 38)
There is very little data for the interstitial charge states; it is matter of ongoing research. The default values for Si are chosen based on an analysis
of Giles [7]. See Table 4 in the section “Adding SUPREM 3.5’s GaAs
Models and Parameters to SUPREM-IV” for GaAs values.
/silicon, /oxide, /poly, /oxynitr, /nitride, /gaas, /gas
These parameters allow the specification of the interface for which the
boundary condition parameters apply. For example, parameters about the
oxide silicon effect on interstitials should be specified by listing silicon /
oxide. Only one of these can be specified at a time.
164
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INTERSTITIAL
time.inj, growth.inj, recomb
These parameters specify the type of reactions occurring at the specified
interface. The time.inj parameter means that a time dependent injection
model should be chosen. The growth.inj parameter ties the injection to the
interface growth velocity. The recomb parameter indicates a finite surface
recombination velocity.
Ksurf.0, Ksurf.E, Krat.0, Krat.E, Kpow.0, Kpow.E
These parameters allow the specification of the surface recombination velocity. The formula used in computing the actual recombination velocity
is:
K I = K Surf
v ox

 K rat ( B ⁄ A )
K pow

+ 1
(EQ 39)
where vox is the interface velocity, and B/A is the Deal Grove oxide
growth coefficient. (see oxide). The full model applies only to oxide, since
it is the only interface that can grow in SUPREM-IV. This formulation allows an inert interface to have different values than a growing interface.
For inert interfaces, (gas, oxynitride, nitride, poly) KSurf is the only important parameter.
vmole, theta.0, theta.E, Gpow.0, Gpow.E
These parameters allow the specification of generation that is dependent
on the growth rate of the interface. The formula is:
g = θV mole v ox (
v ox
B⁄A
G pow
)
(EQ 40)
Theta, θ, is the fraction of silicon atoms consumed during growth that are
reinjected as interstitials. Vmole is the lattice density of the consumed ma-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
165
INTERSTITIAL
terial. Once again, this model only makes sense for oxide since it is currently the only material which can have a growth velocity.
A.0, A.E, t0.0, t0.E, Tpow.0, Tpow.E
These parameters allow an injection model with a fairly flexible time dependency. The equation for the injection is:
g = A ( t + t0)
T pow
(EQ 41)
where t is the time in the diffusion in seconds. This can be used to represent the injection of interstitials from an oxynitride layer.
rec.str, inj.str
These two string parameters are useful for experimenting with new models for injection or recombination at interfaces. Three macros are defined
for use, t the time in seconds and x and y the coordinates. If these are specified, they are used in place of any other model. For example,
interst silicon /oxide inj.str = (10.0e4 * exp( t / 10.0 ))
describes an injection at the silicon oxide interface that decays exponentially in time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship. This is for use in help supporting future model development, and is
currently not in use.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient fol-
166
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INTERSTITIAL
lows an Arrhenius relationship. This is for use in help supporting future
model development, and is currently not in use.
EXAMPLES
inter silicon Di.0=5.0e-7 D.E=0.0 Cstar.0=1.0e13 Cstar.E=0.0
This statement specifies the silicon diffusion and equilibrium values for
interstitials.
inter sil /oxi growth vmole=5.0e22 theta.0=0.01 theta.E=0.0
This parameter specifies the oxide – silicon interface injection is to be
computed using the oxide growth velocity and with 1% of consumed silicon injected as interstitials.
inter silicon /nitride Ksurf.0=3.5e-3 Ksurf.E=0.0 Krat.0=0.0
This specifies that the surface recombination velocity at the nitride silicon
interface is 3.5×10-3 cm/sec.
inter sil neu.0=1.0 neg.0=1.0 pos.0=0.0
dneg.0=0.0 dpos.0=0.0
inter sil neu.E=0.0 neg.E=0.0 pos.E=0.0
dneg.E=0.0 dpos.0=0.0
This specifies that there are equal numbers of negative and neutral charged
interstitials in intrinsic doping.
BUGS
There are no known bugs in this routine. However, the models used here
are involved in ongoing research, and may by out of date at any time. Further, experimental verification is difficult. Many of the parameters have
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
167
INTERSTITIAL
unknown dependencies on stress, temperature, starting silicon material,
stacking fault density, etc. High concentration phosphorus diffusion is
promising with these models, but the coefficients have not been extracted
to allow good fits to experiment.
REFERENCE
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
2.
3.
4.
5.
6.
7.
8.
9.
168
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
P.B. Griffin and J.D. Plummer, “Process Physics Determining 2-D Impurity Profiles in VLSI Devices,” International Electron Devices Meeting, Los Angeles, p. 522, 1986.
W. Shockley and J.T. Last, “Statistics of the Charge Distribution for a
Localized Flaw in a Semiconductor,” Phys. Rev., 107(2), p. 392, 1957.
S.M. Hu, “On Interstitial and Vacancy Concentrations in Presence of
Injection,” J. Appl. Phys., 57, p. 1069, 1985.
C. Boit, F. Lau and R. Sittig, “Gold Diffusion in Silicon by Rapid Optical Annealing,” Appl. Phys. A, 50, p. 197, 1990.
M.E. Law, “Parameters for Point Defect Diffusion and Recombination,” IEEE Trans. on CAD, Accepted for Publication, Sept., 1991.
M.D. Giles, “Defect Coupled Diffusion at High Concentrations,” IEEE
Trans. on CAD, 8(4), p. 460, 1989.
G.A. Baraff and M. Schluter, “Electronic Structure, Total Energies, and
Abundances of the Elementary Point Defects in GaAs,” Phys. Rev.
Lett., 55, 1327 (1985).
R.W. Jansen, D.S. Wolde-Kidane, and O.F. Sankey, “Energetics and
Deep Levels of Interstitial Defects in the Compound Semiconductors
GaAs, AlAs, ZnSe, and ZnTe,” J. Appl. Phys., 64, 2415 (1988).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
INTERSTITIAL
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
magnesium, phosphorus, selenium, isilicon, tin, vacancy, and zinc
statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
169
MAGNESIUM
COMMAND
MAGNESIUM
Set the coefficients of magnesium kinetics.
SYNOPSIS
magnesium
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dip.0=<n> ] [ Dip.E=<n> ] [ Dipp.0=<n> ] [ Dipp.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of magnesium diffusion and segregation. The diffusion equation for magnesium is:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV p
CI
CI p
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 42)
where CT and CA are the total chemical and active concentrations of magnesium, CA is the total electrically active concentration of magnesium, CV
and CI are the vacancy and interstitial concentrations, the superscript * re-
170
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MAGNESIUM
fers to the equilibrium value, DV and DI are the diffusivities with vacancies and interstitials, and p and ni refer to the hole concentration and the
intrinsic electron concentration respectively. The diffusivities are given
by:
p
p 2

D V = ( 1 − F i ) D X + D p ( ) + D PP ( )

ni
ni 
p
p 2

D I = F i D X + D p ( ) + D PP ( )

ni
ni 
(EQ 43)
(EQ 44)
DX , DP , and DPP are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 45)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the magnesium diffusivity with neutral defects. Dix.0 is the pre-exponential constant
and Dix.E is the activation energy. Dix.0 defaults to 0.0 cm2/sec in gallium
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
171
MAGNESIUM
arsenide, and Dix.E defaults to 0.0 eV in gallium arsenide. DX is calculated
using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP, the beryllium diffusivity with singly positive defects. Dip.0 is the pre-exponential
constant and Dip.E is the activation energy. Dip.0 defaults to 6.1×10-2 cm2/
sec for implanted magnesium in gallium arsenide and 6.8×10-3 cm2/sec for
grown-in magnesium in gallium arsenide, and Dip.E defaults to 2.8 eV for
both in gallium arsenide [1,2,3]. DP is calculated using a standard Arrhenius relationship.
Dipp.0, Dipp.E
These floating point parameters allow the specification of DPP , the magnesium diffusivity with doubly positive defects. Dipp.0 is the pre-exponential constant and Dipp.E is the activation energy. Dipp.0 defaults to
0.0 cm2/sec in gallium arsenide, and Dipp.E defaults to 0.0 eV in gallium
arsenide. DPP is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether magnesium diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 1.0.
implanted, grown.in
Specifies whether the Dix, Dip, Dipp, or Fi coefficients apply to implanted
or grown-in magnesium. If neither is specified then a specified parameter
applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
172
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MAGNESIUM
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are:
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, magnesium is an acceptor.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
173
MAGNESIUM
EXAMPLES
magnesium gaas implanted Dip.0=2.2e-6 Dip.E=1.76
This command changes the positive defect diffusivity for implanted magnesium in gallium arsenide.
magnesium gaas /nitride Seg.0=1126.0 Seg.E=0.91
Trn.0=1.66e-7
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be half the nitride concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. H.G. Robinson, M.D. Deal, and D.A. Stevenson, “Hole Dependent Diffusion of Implanted Mg in GaAs,” Appl. Phys. Lett. 58, p. 2801, 1990.
4. H.G. Robinson, “Diffusion of P-Type Dopants in GaAs,” Stanford University Ph.D. Thesis, 1992.
174
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MAGNESIUM
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, phosphorus, selenium, isilicon, tin, vacancy, and zinc
statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
175
MATERIAL
COMMAND
MATERIAL
Set the coefficients of some materials.
SYNOPSIS
material
( silicon | oxide | poly | oxynitr | nitride | photores |
aluminum )
[ ( wet | dry ) ]
[ Ni.0=<n> ] [ Ni.E=<n> ] [ Ni.Pow=<n> ]
[ eps=<n> ]
[ visc.0=<n> ] [ visc.E=<n> ] [ visc.x=<n> ]
[ Young.m=<n> ] [ Poiss.r=<n> ]
[ lcte=<string> ]
[ intrin.sig=<n> ]
[ act.a=<n> ] [ act.b=<n> ] [ ( n.type | p.type ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of the intrinsic concentration and relative permittivity for all the materials.
silicon | oxide | oxynitride | nitride | poly | photores | aluminu
These parameters indicate the material that the remainder of the parameters apply to.
176
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MATERIAL
wet | dry
These parameters indicate whether the parameters apply to in wet or dry
oxides. When oxide is specified, it also necessary to specify the type of
oxide.
Ni.0, Ni.E, Ni.Pow
These parameters specify the dependencies of the intrinsic electron concentration as a function of temperature.
n i = N i .0 e
( − N i .E ⁄ kT )
T
N i .pow
(EQ 46)
Ni.0 is the pre-exponential term, Ni.E is the activation energy, and Ni.pow
is the power dependence of temperature. The default in silicon is Ni.0 =
3.9×1016 cm3, Ni.E = 0.605 eV, and Ni.Pow = 1.5.
eps
This parameter allows the specification of the relative permittivity of the
different materials.
visc.0, visc.E, visc.x
These are the parameters specifying viscosity. visc.0 is the pre-exponential coefficient, visc.E is the activation energy. visc.x is the incompressibility factor. Normally this is left at the value of 0.499 (0.5 is infinitely
incompressible), but if it is desired to allow more compressibility, it can be
lowered.
Young.m, Poiss.r
Young.m is the material's Young's modulus, in dynes/cm2. Poiss.r is the
material's Poisson ratio.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
177
MATERIAL
lcte
This is an expression giving the linear coefficient of thermal expression as
a function of temperature, called T in the expression. It is given as a fraction, not as a percentage.
intrin.sig
This parameter specifies the initial uniform stress state of a material such
as a thin film of nitride deposited on the substrate. It can be specified as a
function of temperature by using an expression and the variable T (see examples).
act.a, act.b
GaAs activation modeling includes a compensation mechanism. This is
modeled in SUPREM-IV.GS using the following expression:
( N D − N A ) effective =
A ( ND − NA)
1 + ( ND − NA) ⁄ B
(EQ 47)
Where A and B in the above expression are set by the act.a and act.b parameters. act.a and act.b may be expressions in terms of T, the temperature in degrees C. The values of A and B are dependent upon the local
dominant impurity type so that one of the p.type or n.type parameters
must be specified when specifying act.a or act.b.
n.type, p.type
When setting the GaAs activation coefficients using the act.a and act.b
parameters, one of the n.type or p.type parameters must be specified to indicate the type of region that they are to apply to.
178
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
MATERIAL
EXAMPLES
material silicon eps = 11.9
This statement specifies the silicon relative permittivity.
mate nitride lcte=(3e-6+2*1e-10*T)
intrin.sig=1.4e10 You=3e12
This statement gives the thermal expansion coefficient of nitride as a function of absolute temperature T. Thus at 0˚K the coefficient is 0.0003%/˚K.
The initial stress in the nitride film is 1.4×1010 dynes/cm2 and the Young's
modulus is 3×1012 dynes/cm2.
BUGS
There is limitation in the kind of temperature dependence ni can take on. It
is limited to expressions of the form above. It should be done in the same
fashion as the coefficient of expansion.
SEE ALSO
The oxide, stress, and diffuse statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
179
OXIDE
COMMAND
OXIDE
Specify oxidation coefficients.
SYNOPSIS
oxide
orientation= ( 111 | 110 | 100 )
( dry | wet )
[ lin.l.0=<n> ] [ lin.l.e=<n> ] [ lin.h.0=<n> ] [ lin.h.e=<n> ]
[ l.break=<n> ] [ l.pde=<n> ]
[ par.l.0=<n> ] [ par.l.e=<n> ] [ par.h.0=<n> ] [ par.h.e=<n> ]
[ p.break=<n> ] [ p.pdep=<n> ]
[ ori.dep ] [ ori.fac=<n> ]
[ thinox.0=<n> ] [ thinox.e=<n> ] [ thinox.l=<n> ]
[ hcl.pc=<n> ] [ hclT=<string> ] [ hclP=<string> ]
[ hcl.par=<string> ] [ hcl.lin=<string> ]
[ baf.dep ] [ baf.ebk=<n> ] [ baf.pe=<n> ] [ baf.ppe=<n> ]
[ baf.ne=<n> ] [ baf.nne=<n> ] [ baf.k0=<n> ] [ baf.ke=<n> ]
[ stress.dep ] [ Vc=<n> ] [ Vr=<n> ] [ Vd=<n> ] [ Vt=<n> ]
[ Dlim=<n> ]
[ gamma=<n> ] [ alpha=<n> ]
[ henry.coeff=<n> | theta=<n> ]
[ ( silicon | oxide | nitride | poly | gaas | gas ) ]
[ ( /silicon | /oxide | /nitride | /poly | /gaas | /gas ) ]
[ diff.0=<n> ] [ diff.e=<n> ] [ seg.0=<n> ] [ seg.E=<n> ]
[ trn.0=<n> ] [ trn.E=<n> ]
[ initial=<n> ] [ spread=<n> | mask.edge=<n> ]
[ erf.q=<n> ] [ erf.delta=<n> ] [ erf.lbb=<n> ] [ erf.h=<n> ]
[ nit.thick=<n> ]
180
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
OXIDE
DESCRIPTION
All parameters relating to oxidation, and a few more besides, are specified
here. Five oxide models are supported in this release: 1) an error-function
fit to bird's beak shapes; 2) a parameterized error-function model from the
literature; 3) a model where oxidant diffuses and the oxide boundaries
move vertically at a rate determined by the local oxidant concentration; 4)
a compressible viscous flow model, similar to 3 but in addition the new
oxide formed at each time step forces the overlying oxide (and nitride) to
flow; 5) an incompressible viscous flow model.
The error function is by far the fastest. It should be used for uniform oxidation, and is the most reliable for semi-recessed oxidation. It requires fitting data for the lateral spread of the bird's beak.
The parameterized model is by Guillemot [1]. The bird's beak length and
nitride lifting were measured as a function of process conditions.
The diffusion model has no fitting parameters, but is only accurate when
the growth is reasonably vertical – less than say 30˚ interface angle.
The compressible model is more accurate, but requires more computer
time. It is still cheaper than the incompressible model, which uses many
more grid points. The incompressible model is required whenever accurate
stresses are desired.
Most coefficients need to know whether wet or dry oxidation is intended,
and some need to know what the substrate orientation is.
orientation
The substrate orientation to which the coefficients specified apply. Required for orientation factor (see below) and thin oxide coefficients.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
181
OXIDE
dry | wet
The type of oxidation to which the specified coefficients apply. Required
for everything except for the one-dimensional coefficients and the volume
ratio.
lin.l.0, lin.l.e, lin.h.0, lin.h.e, l.break, l.pdep
The linear rate coefficients (B/A). A doubly activated Arrhenius model is
assumed. l.break is the temperature breakpoint between the lower and
higher ranges, in degrees Celsius. lin.l.0 is the prefactor in µm/min, and
lin.l.e is the activation energy in eV for the low temperature range. lin.h.0
and lin.h.e are the corresponding high temperature numbers. l.pdep is the
exponent of the pressure dependence. The value given is taken to apply to
<111> orientation and later adjusted by ori.fac according to the substrate
orientation present.
par.l.0, par.l.e, par.h.0, par.h.e, p.break, p.pdep
The parabolic rate coefficients (B). Like the linear rate coefficients, but
different.
ori.dep, ori.fac
The numerical coefficient ori.fac is the ratio of B/A on the specified orientation to that on the <111> orientation. The boolean parameter ori.dep
(defaults true) specifies whether the local orientation at each point on the
surface should be used to calculate B/A. If it is false, the substrate orientation is used at all points.
thinox.0, thinox.e, thinox.l
Coefficients for the thin oxide model proposed by Massoud [2]. thinox.0
is the prefactor in µm/min, thinox.e is the activation energy in eV, and thinox.l is the characteristic length in µm.
182
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
OXIDE
hcl.pc, hclT, hclP, hcl.par, hcl.lin
The numerical parameter hcl.pc is the percentage of HCl in the gas
stream. It defaults to 0. The HCl dependence of the linear and parabolic
coefficients is obtained from a look-up table specified in the model file.
The rows of the table are indexed by HCl percentage. The row entries can
be specified with the parameter hclP, which is an array of numerical values, surrounded by double quotes and separated by spaces or commas. The
columns are indexed by temperature. The column entries can be specified
with the parameter hclT, which is an array of numerical values, surrounded by double quotes and separated by spaces or commas. The dependence
of B/A can be specified with the parameter hcl.lin, which is an array of numerical values, surrounded by double quotes and separated by spaces or
commas. The number of entries in hcl.lin must be the product of the number of entries in hclP and hclT. The dependence of B can be specified with
the parameter hcl.par, which is an array of numerical values, surrounded
by double quotes and separated by spaces or commas. The number of entries in hcl.par must be the product of the number of entries in hclP and
hclT.
baf.dep, baf.ebk, baf.pe, baf.ppe, baf.ne, baf.nne, baf.k0, baf.ke
These parameters relate to the doping dependence of the oxidation rate.
The doping dependence is turned on if baf.dep is true. The linear rate coefficient, B/A, is assumed to depend on the Fermi level as follows [3].
B ⁄ A = ( B ⁄ A ) 0 [ 1 + K ( [V ] ⁄ [V ] 0 − 1 ) ]
(EQ 48)
[V ] is the total concentration of vacancies and K is an activated coefficient
with prefactor baf.k0 and activation energy baf.ke. The remaining parameters above serve to compute [V ]. The total concentration of vacancies
[V ] is the sum of the concentrations in each charge state (see vacancies).
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
183
OXIDE
stress.dep, Vc, Vr, Vd, Vt, Dlim
These parameters control the stress dependence of oxidation, which is
only calculated under the viscous model. The parameter stress.dep turns
on the dependence. The parameter Vc is the activation volume of viscosity. The parameter Vr is the activation volume of the reaction rate with respect to normal stress. The parameter Vt is the activation volume of the
reaction rate with respect to tangential stress. The parameter Vd is the activation volume of oxidant diffusion with respect to pressure. The parameter
Dlim is the maximum increase of diffusion permitted under tensile stress.
gamma
The parameter gamma is the oxidant surface energy in ergs/cm2, which
controls reflow.
alpha
The volume expansion ratio between material 1 and material 2. In a nutshell, alpha oxide /silicon is 2.2, and alpha x /y is 1.0 for everything else
(until someone tells us otherwise).
silicon | oxide | nitride | poly | gaas | gas
What material 1 is.
/silicon | /oxide | /nitride | /poly | /gaas | /gas
What material 2 is.
henry.coeff | theta
Henry's coefficient is the solubility of oxidant in material 1 at one atmosphere, in cm-3. Theta is the number of oxygen atoms incorporated in a
cubic centimeter of oxide. Note: Don't change these unless you really
know what you are doing. Change the Deal-Grove coefficients instead.
184
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
OXIDE
diff.0, diff.e, seg.0, seg.E, trn.0, trn.E
The diffusion coefficients of oxidant in material 1, and the boundary coefficients (“transport” and “segregation”) from material 1 to material 2. See
the note above. For the record, diff.0 is the diffusivity prefactor in cm2/sec,
diff.e is the energy in eV. The transport coefficient represents the gasphase mass-transfer coefficient in terms of concentrations in the solid at
the oxide-gas interface, the chemical surface-reaction rate constant at the
oxide-silicon surface, and a regular diffusive transport coefficient at other
interfaces. The segregation coefficient is 1 at the oxide-gas interface, infinity at the oxide-silicon interface, and represents a regular segregation coefficient at other interfaces.
initial
The thickness of the existing oxide at the start of oxidation, default 2 nm.
If the wafer is bare, an oxide layer of this thickness is deposited before oxidation begins.
spread | mask.edge
These coefficients are only used in the error-function approximation to a
bird's beak shape. Spread is the relative lateral to vertical extension, defaults to 1. It's a fitting parameter to make erfc birds look realistic.
Mask.edge is the position of the mask edge in microns, and defaults to
negative infinity. Oxide grows to the right of the mask edge.
erf.q, erf.delta, erf.lbb, erf.h, nit.thick
This group of parameters all apply to the “erfg” model. See Guillemot et
al. for their interpretation.
erf.q, erf.delta
The delta and q parameters for the “erfg” model. These probably do not
need to be changed, but they're available if you want them.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
185
OXIDE
erf.lbb
The erf.lbb parameter is the length of the bird's beak. It can be specified as
an expression in Eox (the field oxide thickness (µm)), eox (the pad oxide
thickness (µm)), Tox (the oxidation temperature (Kelvin)), and en (the nitride thickness (µm)). The published expression can be found in the models file. Specifying “erf.llbb=Eox” for instance would give a lateral spread
equal to the field thickness, similar to the Hee-Gook Lee model with a
spread of 1.
erf.h
The erf.h parameter is the ratio of the nitride lifting to the field oxide
thickness. (It corresponds to the Guillemot “H” parameter except that it is
normalized to the field oxide thickness). Again it is specified as an expression of Eox, eox, Tox, en.
nit.thick
The nitride thickness to substitute for the parameter “en”.
EXAMPLES
Look at the models file for a huge example.
BUGS
In increasing order of severity:
If a required parameter is omitted, like orientation when a linear rate coefficient is being specified, the statement is ignored without warning.
The volume expansion data should be on the material statement.
186
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
OXIDE
Oxidant in materials other than oxide is allowed to diffuse and segregate,
but its concentration is then ignored (no oxynitridation, for instance). The
diffusion and transport coefficients in oxide to gas and silicon are derived
from the Deal-Grove coefficients, so these parameters are ignored if read
from input statements.
The non-analytic oxide models don't account for the thin oxide correction
in dry oxygen.
The analytic models use the “thickness” of the oxide to compute the
growth rate. In addition, the “erfg” model uses the nitride thickness. These
values are NOT inferred from the structure. Instead, the nitride thickness
is taken from the user on the oxide command, and the oxide thickness is
computing by adding the total oxide grown to the initial oxide thickness
specified on the oxide command. If the structure at the start of diffusion
has more than the default 20 angstroms of native oxide on it, that thickness
must be specified by the user. Beware of this when continuing a diffusion
by any means (e.g. after reading in a previous structure). A “diffuse” followed by “diffuse continue=t” will however do the right thing.
References
1. N. Guillemot, G. Pananakakis and P. Chenevier, “A New Analytical
Model of the ``Bird's Beak'',” IEEE Transactions on Electron Devices,
ED-34, 1987.
2. H.Z. Massoud, J.D. Plummer and E.A. Irene, “Thermal Oxidation of
Silicon in Dry Oxygen Growth Rate Enhancement in the Thin Regime,” J. Electrochem. Soc., 132, p. 2685, 1985.
3. C.P. Ho and J.D. Plummer, “Si/SiO2 Interface Oxidation Kinetics: A
Physical Model for the Influence of High Substrate Doping Levels,
Parts I and II,” J. Electrochem. Soc., 126, p. 1523, 1979.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
187
PHOSPHORUS
COMMAND
PHOSPHORUS
Set the coefficients of phosphorus kinetics.
SYNOPSIS
phosphorus
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ]
[ Dvx.0=<n> ] [ Dvx.E=<n> ]
[ Dvm.0=<n> ] [ Dvm.E=<n> ]
[ Dvmm.0=<n> ] [ Dvmm.E=<n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of phosphorus diffusion and segregation. The diffusion equation for phosphorus is
[1,2]:
∂C T
∂t
188
= ∇ DV CT
CV
*
CV
CV n
CI
CI n
∇ln C T *  + D I C T * ∇ln C T * 
 CV ni 
 CI ni 
CI
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
(EQ 49)
PHOSPHORUS
where CT is the total chemical concentration of phosphorus, CV and CI are
the vacancy and interstitial concentrations, the superscript * refers to the
equilibrium concentration, DV and DI are the diffusivities with vacancies
and interstitials, and n and ni refer to the electron concentration and the intrinsic concentration respectively. The diffusivities are given by:
2
D V = D VX + D VM n + D VMM ( n )
ni
ni
(EQ 50)
2
D I = D IX + D IM n + D IMM ( n )
ni
ni
(EQ 51)
DIX , DIM , DIMM , DVX , DVM , and DVMM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1 −

M 12 
(EQ 52)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
189
PHOSPHORUS
Dix.0, Dix.E
These floating point parameters allow the specification of the phosphorus
diffusing with interstitial neutral defects. Dix.0 is the pre-exponential constant and Dix.E is the activation energy. Dix.0 defaults to 3.85 cm2/sec in
silicon, and Dix.E defaults to 3.66 eV in silicon [3]. DX is calculated using
a standard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the phosphorus
diffusing with singly negative interstitial defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to
4.44 cm2/sec in silicon, and Dim.E defaults to 4.00 eV in silicon [3]. DM is
calculated using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of the phosphorus
diffusing with doubly negative interstitial defects. Dimm.0 is the pre-exponential constant and Dimm.E is the activation energy. Dimm.0 defaults
to 44.2 cm2/sec in silicon, and Dim.E defaults to 4.37 eV in silicon [3].
DMM is calculated using a standard Arrhenius relationship.
Dvx.0, Dvx.E
These floating point parameters allow the specification of the phosphorus
diffusing with neutral vacancy defects. Dvx.0 is the pre-exponential constant and Dvx.E is the activation energy. Both of these are 0.0, since phosphorus is an interstitial diffuser [4].
Dvm.0, Dvm.E
These floating point parameters allow the specification of the phosphorus
diffusing with singly negative vacancy defects. Dvm.0 is the pre-exponential constant and Dvm.E is the activation energy. Both of these are 0.0,
since phosphorus is an interstitial diffuser [4].
190
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PHOSPHORUS
Dvmm.0, Dvmm.E
These floating point parameters allow the specification of the phosphorus
diffusing with doubly negative vacancy defects. Dvmm.0 is the pre-exponential constant and Dvmm.E is the activation energy. Both of these are
0.0, since phosphorus is an interstitial diffuser [4].
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, Dvx, Dvm, Dvmm, or Fi coefficients apply to implanted or grown-in phosphorus. If neither is specified
then a specified parameter applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are [5]:
ss.temp
ss.conc
800˚C
2.79×1020 cm-3
900˚C
3.16×1020 cm-3
1000˚C
3.40×1020 cm-3
1100˚C
3.80×1020 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
191
PHOSPHORUS
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default phosphorus is a donor.
EXAMPLES
phosphorus silicon Dix.0=3.85 Dix.E=3.65
This command changes the neutral defect diffusivity in silicon.
phosphorus silicon /oxide Seg.0=30.0 Trn.0=1.66e-7
Seg.E=0.0
This command will change the segregation parameters at the silicon – silicon dioxide interface. The silicon concentration will be 30.0 times the oxide concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
192
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
PHOSPHORUS
REFERENCES
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
2.
3.
4.
5.
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
D. Mathiot and J.C. Pfister, “Dopant Diffusion in Silicon: A consistent
view involving nonequilibrium defects,” J. Appl. Phys., 55(10), p.
3518, 1984.
R.B. Fair, “Concentration Profiles of Diffused Dopants in Silicon,” Impurity Doping Processes in Silicon, Yang ed., 1981, North-Holland,
New York.
P. Fahey, G. Barbuscia, M. Moslehi and R.W. Dutton, “Kinetics of
Thermal Nitridation Processes in the Study of Dopant Diffusion Mechanisms in Silicon,” Appl. Phys. Lett., 46(8), p. 784, 1985.
F.A. Trumbore, “Solid Solubilities of Impurity Elements in Germanium
and Silicon,” Bell System Tech Journal, 1960.
SEE ALSO
The antimony, arsenic, boron, interstitial, and vacancy statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
193
SELENIUM
COMMAND
SELENIUM
Set the coefficients of selenium kinetics.
SYNOPSIS
selenium
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ] [ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of selenium diffusion and segregation. The diffusion equation for selenium is:
∂C T
∂t
= ∇ DV CA
CV
C
C
C
 C V n  + D C I ∇ln C I n 
∇ln
A
I
A
A
*
*
 C *V n i 
 C *I n i 
CV
CI
(EQ 53)
where CT and CA are the total chemical and active concentrations of selenium, CV and CI are the vacancy and interstitial concentrations, the superscript * refers to the equilibrium concentration, DV and DI are the
diffusivities with vacancies and interstitials, and n and ni refer to the elec-
194
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
SELENIUM
tron concentration and the intrinsic concentration respectively. The diffusivities are given by:
n
n 2

D V = ( 1 − F i ) D X + D M ( ) + D MM ( )

ni
ni 
(EQ 54)
n
n 2

D I = F i D X + D M ( ) + D MM ( )

ni
ni 
(EQ 55)
DX , DM , and DMM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 56)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the selenium
diffusing with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. For implanted selenium in gallium arsenide
Dix.0 defaults to 1.8×10-8 cm2/sec and Dix.E defaults to 1.6 eV. For grownin selenium in gallium arsenide Dix.0 defaults to 0.0 cm2/sec and Dix.E de-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
195
SELENIUM
faults to 0.0 eV [1,2,3]. DX is calculated using a standard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the selenium
diffusing with singly negative defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to 0.0 cm2/sec in
gallium arsenide, and Dim.E defaults to 0.0 eV in gallium arsenide. DM is
calculated using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of the selenium
diffusing with doubly negative defects. Dimm.0 is the pre-exponential
constant and Dimm.E is the activation energy. For implanted selenium in
gallium arsenide Dimm.0 defaults to 0.0 cm2/sec and Dimm.E defaults to
0.0 eV. For grown-in selenium in gallium arsenide Dimm.0 defaults to 1.2
cm2/sec and Dimm.E defaults to 3.6 eV [1,2,3]. DMM is calculated using a
standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether selenium diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.0.
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, or Fi coefficients apply to implanted or grown-in selenium. If neither is specified then a specified parameter
applies to both.
ss.clear
This parameter clears the currently stored solid solubility data.
196
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
SELENIUM
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, selenium is an donor.
EXAMPLES
selenium gaas implanted Dimm.0=2.1e-3 Dimm.E=3.1
This command changes the doubly negative defect diffusivity for implanted selenium in silicon.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
197
SELENIUM
selenium gaas /nitride Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be 30.0 times the nitride concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. M.D. Deal, S.E. Hansen, and T.W. Sigmon, “SUPREM 3.5 – Process
Modeling of GaAs Integrated Circuit Technology,” IEEE Trans. CAD,
9, p. 939, 1989.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, magnesium, phosphorus, isilicon, tin, vacancy, and zinc
statements.
198
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
iSILICON
COMMAND
iSILICON
Set the coefficients of silicon impurity kinetics.
SYNOPSIS
isilicon
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ] [ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of silicon
impurity diffusion and segregation. The diffusion equation for silicon impurities are:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV n
CI
CI n
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 57)
where CT and CA are the total chemical and active concentrations of silicon, CV and CI are the vacancy and interstitial concentrations, the superscript * refers to the equilibrium concentration, DV and DI are the
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
199
iSILICON
diffusivities with vacancies and interstitials, and n and ni refer to the electron concentration and the intrinsic concentration respectively. The diffusivities are given by:
n
n 2

D V = ( 1 − F i ) D X + D M ( ) + D MM ( )

ni
ni 
n
n 2

D I = F i D X + D M ( ) + D MM ( )

ni
ni 
(EQ 58)
(EQ 59)
DX , DM , and DMM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 60)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the silicon diffusing with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. For implanted silicon in gallium arsenide
200
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
iSILICON
Dix.0 defaults to 1.8×10-9 cm2/sec and Dix.E defaults to 1.6 eV. For grown-
in silicon in gallium arsenide Dix.0 defaults to 0.0 cm2/sec and Dix.E defaults to 0.0 eV [1,2,3]. DX is calculated using a standard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the silicon diffusing with singly negative defects. Dim.0 is the pre-exponential constant
and Dim.E is the activation energy. Dim.0 defaults to 0.0 cm2/sec in gallium arsenide, and Dim.E defaults to 0.0 eV in gallium arsenide. DM is calculated using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of the silicon diffusing with doubly negative defects. Dimm.0 is the pre-exponential constant and Dimm.E is the activation energy. For implanted silicon in
gallium arsenide Dimm.0 defaults to 0.0 cm2/sec and Dimm.E defaults to
0.0 eV. For grown-in silicon in gallium arsenide Dimm.0 defaults to
33.0 cm2/sec and Dimm.E defaults to 3.9 eV [1,2,3]. DMM is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether silicon diffuses through interaction with interstitials or vacancies. The value of Fi defaults to 0.0.
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, or Fi coefficients apply to implanted or grown-in silicon. If neither is specified then a specified parameter
applies to both.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
201
iSILICON
ss.clear
This parameter clears the currently stored solid solubility data.
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, silicon is an donor.
202
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
iSILICON
EXAMPLES
isilicon gaas implanted Dimm.0=2.1e-3 Dimm.E=3.1
This command changes the doubly negative defect diffusivity for implanted silicon in gallium arsenide.
isilicon gaas /nitride Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be 30.0 times the nitride concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. E.L. Allen, J.J. Murray, M.D. Deal, J.D. Plummer, K.S.Jones, and W.S.
Robert, “Diffusion of Ion-Implanted Group IV Dopants in GaAs,” J.
Electrochem. Soc., 138, p. 3440, 1991.
4. J.J. Murray, M.D. Deal, E.A. Allen, D.D. Stevenson, and S. Nozaki,
“Modeling Silicon Diffusion in GaAs Using Well Defined Silicon
Doped Molecular Beam Epitaxy Structures,” J. Electrochem. Soc., 139,
p. 2037, 1992.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
203
iSILICON
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, magnesium, phosphorus, selenium, tin, vacancy, and zinc
statements.
204
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
TIN
COMMAND
TIN
Set the coefficients of tin kinetics.
SYNOPSIS
tin
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ] [ Dim.0=<n> ] [ Dim.E=<n> ]
[ Dimm.0=<n> ] [ Dimm.E=<n> ] [ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of tin diffusion and segregation. The diffusion equation for tin is:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV n
CI
CI n
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 61)
where CT and CA are the total chemical and active concentrations of tin,
CV and CI are the vacancy and interstitial concentrations, the superscript *
refers to the equilibrium concentration, DV and DI are the diffusivities
with vacancies and interstitials, and n and ni refer to the electron concen-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
205
TIN
tration and the intrinsic concentration respectively. The diffusivities are
given by:
n
n 2

D V = ( 1 − F i ) D X + D M ( ) + D MM ( )

ni
ni 
(EQ 62)
n
n 2

D I = F i D X + D M ( ) + D MM ( )

ni
ni 
(EQ 63)
DX , DM , and DMM are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 64)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of the tin diffusing
with neutral defects. Dix.0 is the pre-exponential constant and Dix.E is the
activation energy. Dix.0 defaults to 0.0 cm2/sec in gallium arsenide, and
206
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
TIN
Dix.E defaults to 0.0 eV in gallium arsenide. D is calculated using a stanX
dard Arrhenius relationship.
Dim.0, Dim.E
These floating point parameters allow the specification of the tin diffusing
with singly negative defects. Dim.0 is the pre-exponential constant and
Dim.E is the activation energy. Dim.0 defaults to 0.0 cm2/sec in gallium arsenide, and Dim.E defaults to 0.0 eV in gallium arsenide. DM is calculated
using a standard Arrhenius relationship.
Dimm.0, Dimm.E
These floating point parameters allow the specification of the tin diffusing
with doubly negative defects. Dimm.0 is the pre-exponential constant and
Dimm.E is the activation energy. Dimm.0 defaults to 96.0 cm2/sec in gallium arsenide, and Dimm.E defaults to 3.9 eV in gallium arsenide [1,2,3].
DMM is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether tin diffuses through interaction with interstitials or
vacancies. The value of Fi defaults to 0.0.
implanted, grown.in
Specifies whether the Dix, Dim, Dimm, or Fi coefficients apply to implanted or grown-in tin. If neither is specified then a specified parameter applies
to both.
ss.clear
This parameter clears the currently stored solid solubility data.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
207
TIN
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. M12 is calculated using a standard Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, tin is an donor.
EXAMPLES
tin gaas implanted Dimm.0=2.1e-3 Dimm.E=3.1
This command changes the doubly negative defect diffusivity for implanted tin in silicon.
208
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
TIN
tin gaas /nitride Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be 30.0 times the nitride concentration in equilibrium.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
3. E.L. Allen, J.J. Murray, M.D. Deal, J.D. Plummer, K.S.Jones, and W.S.
Robert, “Diffusion of Ion-Implanted Group IV Dopants in GaAs,” J.
Electrochem. Soc., 138, p. 3440, 1991.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, magnesium, phosphorus, selenium, isilicon, vacancy, and
zinc statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
209
TRAP
COMMAND
TRAP
Set coefficients of interstitial traps.
SYNOPSIS
trap
( silicon | oxide | poly | oxynitr | nitride | gas |
aluminum | photores )
[ enable ]
[ total=<n> ]
[ frac.0=<n> ] [ frac.E=<n> ]
DESCRIPTION
This statement allows the user to specify values for coefficients of the interstitial traps. The statement allows coefficients to be specified for each of
the materials. SUPREM-IV has default values only for silicon. Polysilicon
has not been characterized as extensively, and its parameters default to
those for silicon.
The trap reaction was described by Griffin[1]. This model explains some
of the wide variety of diffusion coefficients extracted from several different experimental conditions. The trap equation is:
∂C ET
∂t
210
= − K T C ET C I −
e*
1−
e*
*
C I ( C T − C ET )
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
(EQ 65)
TRAP
where CT is the total trap concentration, KT is the trap reaction coefficient,
e* is the equilibrium trap occupancy ratio. Instead of the reaction, the time
derivative is used in the interstitial equation because it has better properties in the numerical calculation. The equation is derived from a simple interaction of an interstitial and a trap. To achieve balance in equilibrium, e*
is defined to be CET / CT, the equilibrium number of empty traps divided
by the total traps.
silicon, oxide, poly, oxynitr, nitride, gas, aluminum, photores
These parameters allow the specification of the material for which the parameters apply.
enable
This indicates that material specified has a finite number of traps.
total
This floating point parameter is used to specify the total number of traps,
in cm-3. The default for silicon is 2×1018 cm-3. This value is appropriate
for Czochralski silicon material.
frac.0, frac.E
These floating point parameters allow the specification of the equilibrium
empty trap ratio, e*. The default for these parameters is 2.39×105 cm-3 and
1.57 eV for the pre-exponential and activation energy for silicon.
EXAMPLES
trap silicon total=2.0e18 frac.0=0.5 frac.E=0.0 enable
This statement turns on interstitial traps and sets the total to 2×1018 and
the fraction to a half.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
211
TRAP
BUGS
There are no known bugs in this model. However, the model used here is
involved in ongoing research, and may by out of date at any time. Further,
experimental verification is difficult. The trap concentration will depend
on the thermal history of the wafer, starting material, stress and temperature.
REFERENCE
1. P.B. Griffin and J.D. Plummer, “Process Physics Determining 2-D Im-
purity Profiles in VLSI Devices,” International Electron Devices Meeting, Los Angeles, p. 522, 1986.
SEE ALSO
The interstitial and vacancy statements.
212
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
VACANCY
COMMAND
VACANCY
Set coefficients of vacancy kinetics.
SYNOPSIS
vacancy
( silicon | oxide | poly | oxynitr | nitride | gaas | gas )
[ D.0=<n> ] [ D.E=<n> ]
[ Kr.0=<n> ] [ Kr.E=<n> ]
[ Cstar.0=<n> ] [ Cstar.E=<n> ]
[ ktrap.0=<n> ] [ ktrap.E=<n> ]
[ neu.0=<n> ] [ neu.E=<n> ]
[ neg.0=<n> ] [ neg.E=<n> ] [ dneg.0=<n> ] [ dneg.E=<n> ]
[ tneg.0=<n> ] [ tneg.E=<n> ]
[ pos.0=<n> ] [ pos.E=<n> ] [ dpos.0=<n> ] [ dpos.E=<n> ]
[ tpos.0=<n> ] [ tpos.E=<n> ]
[ ( /silicon | /oxide | /poly | /oxynitr | /nitride | /gaas |
/gas ) ]
[ time.inj ] [ growth.inj ] [ recomb ]
[ Ksurf.0=<n> ] [ Ksurf.E=<n> ]
[ Krat.0=<n> ] [ Krat.E=<n> ]
[ Kpow.0=<n> ] [ Kpow.E=<n> ]
[ vmole=<n> ] [ theta.0=<n> ] [ theta.E=<n> ]
[ Gpow.0=<n> ] [ Gpow.E=<n> ]
[ A.0=<n> ] [ A.E=<n> ] [ t0.0=<n> ] [ t0.E=<n> ]
[ Tpow.0=<n> ] [ Tpow.E=<n> ]
[ rec.str=<s> ] [ inj.str=<s> ]
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
213
VACANCY
DESCRIPTION
This statement allows the user to specify values for coefficients of the vacancy continuity equation. The statement allows coefficients to be specified for each of the materials. Of course, the meaning of a lattice vacancy
in an amorphous region is a philosophical topic. SUPREM-IV has default
values only for silicon and the interfaces with silicon and gallium arsenide
and its interfaces. Polysilicon has not been characterized as extensively,
and its parameters default to those for silicon.
The vacancies obey a complex continuity equation which can be written
[1]:
∂C V
∂t
= ∇ ( − JV −
∑J
AV )
−R
(EQ 66)
imp
where CV is the vacancy concentration, JV refers to the vacancy flux, JAV
refers to the flux of impurity A diffusing with vacancies, and R is all
sources of bulk recombination of vacancies. In the two.dim model (see
method) the fluxes from the dopants, JAV , are ignored. Only in the full.cpl
model are they computed and included in the vacancy equation. This model represents the diffusion of all vacancies, paired or unpaired, and can be
derived from assuming thermal equilibrium between the species and that
the simple pairing reactions are dominant [1].
The pair fluxes are the vacancy portions of the flux as described in each of
the models for the impurities (see the various impurity statements). The
vacancy flux can be written [1]:
*
−JV = DV CV ∇
214
CV
*
CV
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
(EQ 67)
VACANCY
It is important to note that the equilibrium concentration, C*V, is a function
of Fermi level [3]. This flux accounts correctly for the effect of an electric
field on the charged portion of the defect concentration. The bulk recombination is simple interaction between interstitials and vacancies. This can
be expressed:
*
*
R = KR ( CI CV − CI CV)
(EQ 68)
where KR is the bulk recombination coefficient, and CI and C*I are the interstitial and interstitial equilibrium concentration, respectively.
The defects obey a flux balance boundary condition, as described by Hu
[4]:
*
JV n + KV ( CV − CV) = g
(EQ 69)
where n is the surface normal, KV is the surface recombination constant,
and g is the generation, if any, at the surface. This expression has been
used with success on several different surface types.
silicon, oxide, poly, oxynitr, nitride, gaas, gas
These parameters allow the specification of the material for which the parameters apply.
D.0, D.E
These floating point parameters are used to specify the diffusion coefficient of the vacancies. The units are in cm2/sec. The default values are
6.34×103 cm2/sec and 3.29 eV [5] for silicon, and 1.0×10-12 cm2/sec and
0.0 eV for GaAs.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
215
VACANCY
Kr.0, Kr.E
These floating point parameters allow the specification of the bulk recombination rate in cm3/sec. The default is 1.4 cm3/sec and 3.99 eV [6] for silicon, and 1.0×10-18 cm3/sec and 0.0 eV for GaAs.
Cstar.0, Cstar.E
These parameters allow the specification of the total equilibrium concentration of vacancies in intrinsically doped conditions. The default values
are 4.77×1018 cm-3 and 0.713 eV [5] for silicon, and 4.77×1014 cm-3 and
0.0 eV for GaAs.
neu.0, neu.E, neg.0, neg.E, dneg.0, dneg.E, tneg.0, tneg.E,
pos.0, pos.E, dpos.0, dpos.E, tpos.0, tpos.E
These values allow the user to specify the relative concentration of interstitials in the various charge states (neutral, negative, double negative, triple negative, positive, double positive, and triple positive) under intrinsic
doping conditions. For example, in intrinsic conditions, the concentration
of doubly negative interstitials is given by:
C Star dneg
=
CI =
(EQ 70)
neu + neg + dneg + tneg + pos + dpos + tpos
where CStar is the total equilibrium concentration in intrinsic doping conditions. In extrinsic conditions, the total equilibrium concentration is given
by [3]:
2
neu + neg
*
C I = C Star
3
2
n
n
n
p
p
p
+ dneg ( ) + tneg ( ) + pos + dpos ( ) + tpos ( )
ni
ni
ni
ni
ni
ni
neu + neg + dneg + tneg + pos + dpos + tpos
3
(EQ 71)
There is very little data for the vacancy charge states; it is matter of ongoing research. The default values for silicon are chosen based on an analy-
216
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
VACANCY
sis and measurements of Watkins [7]. See Table 4 in the section “Adding
SUPREM 3.5’s GaAs Models and Parameters to SUPREM-IV” for GaAs
values.
/silicon, /oxide, /poly, /oxynitr, /nitride, /gas, /gaas
These parameters allow the specification of the interface for which the
boundary condition parameters apply. For example, parameters about the
oxide silicon effect on vacancies should be specified by listing silicon /oxide. Only one of these can be specified at a time.
time.inj, growth.inj, recomb
These parameters specify the type of reactions occurring at the specified
interface. The time.inj parameter means that a time dependent injection
model should be chosen. The growth.inj parameter ties the injection to the
interface growth velocity. The recomb parameter indicates a finite surface
recombination velocity.
Ksurf.0, Ksurf.E, Krat.0, Krat.E, Kpow.0, Kpow.E
These parameters allow the specification of the surface recombination velocity. The formula used in computing the actual recombination velocity
is:
K V = K Surf
v ox

 K rat ( B ⁄ A )
K pow

+ 1
(EQ 72)
where vox is the interface velocity, and B/A is the Deal Grove oxide
growth coefficient. (see oxide). The full model applies only to oxide, since
it is the only interface that can grow in SUPREM-IV. This formulation allows an inert interface to have different values than a growing interface.
For inert interfaces, (gas, oxynitride, nitride, poly) KSurf is the only important parameter.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
217
VACANCY
vmole, theta.0, theta.E, Gpow.0, Gpow.E
These parameters allow the specification of generation that is dependent
on the growth rate of the interface. The formula is:
g = θV mole v ox (
v ox
B⁄A
G pow
)
(EQ 73)
Theta is the fraction of silicon atoms consumed during growth that are reinjected as vacancies. Vmole is the lattice density of the consumed material. Once again, this model only makes sense for oxide since it is currently
the only material which can have a growth velocity.
A.0, A.E, t0.0, t0.E, Tpow.0, Tpow.E
These parameters allow an injection model with a fairly flexible time dependency. The equation for the injection is:
g = A ( t + t0)
T pow
(EQ 74)
where t is the time in the diffusion in seconds. This can be used to represent the injection of vacancies from an nitride layer.
rec.str, inj.str
These two string parameters are useful for experimenting with new models for injection or recombination at interfaces. Three macros are defined
for use, t the time in seconds and x and y the coordinates. If these are specified, they are used in place of any other model. For example,
vacan silicon /oxide inj.str = (10.0e4 * exp( t / 10.0 ))
describes an injection at the silicon oxide interface that exponentially decays in time.
218
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
VACANCY
EXAMPLES
vacan silicon Di.0=5.0e-7 D.E=0.0 Cstar.0=1.0e13
Cstar.E=0.0
This statement specifies the silicon diffusion and equilibrium values for
vacancies.
vacan sil /oxi growth vmole=5.0e22 theta.0=0.01 theta.E=0.0
This parameter specifies the oxide – silicon interface injection is to be
computed using the oxide growth velocity and with 1% of consumed silicon injected as vacancies.
vacan silicon /nitride Ksurf.0=3.5e-3 Ksurf.E=0.0 Krat.0=0.0
This specifies that the surface recombination velocity at the nitride silicon
interface is 3.5×10-3 cm/sec.
inter sil neu.0=1.0 neg.0=1.0 pos.0=0.0 dneg.0=0.0
dpos.0=0.0
inter sil neu.E=0.0 neg.E=0.0 pos.E=0.0 dneg.E=0.0
dpos.0=0.0
This specifies that there are equal numbers of negative and neutral charged
vacancies in intrinsic doping.
BUGS
There are no known bugs in this routine. However, the models used here
are involved in ongoing research, and may by out of date at any time. Further, experimental verification is difficult. Many of the parameters have
unknown dependencies on stress, temperature, starting silicon material,
stacking fault density, etc. High concentration phosphorus diffusion is
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
219
VACANCY
promising with these models, but the coefficients have not been extracted
to allow good fits to experiment.
REFERENCE
1. M.E. Law and J.R. Pfiester, “Low Temperature Annealing of Arsenic/
2.
3.
4.
5.
6.
7.
8.
Phosphorus Junctions,” IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
P.B. Griffin and J.D. Plummer, “Process Physics Determining 2-D Impurity Profiles in VLSI Devices,” International Electron Devices Meeting, Los Angeles, p. 522, 1986.
W. Shockley and J.T. Last, “Statistics of the Charge Distribution for a
Localized Flaw in a Semiconductor,” Phys. Rev., 107(2), p. 392, 1957.
S.M. Hu, “On Interstitial and Vacancy Concentrations in Presence of
Injection,” J. Appl. Phys., 57, p. 1069, 1985.
T.Y. Tan and U. Gösele, “Point Defects, Diffusion Processes, and Swirl
Defect Formation in Silicon,” J. Appl. Phys., 37(1), p. 1, 1985.
M.E. Law, “Parameters for Point Defect Diffusion and Recombination,” IEEE Trans. on CAD, Accepted for Publication, Sept., 1991.
G.D. Watkins, “EPR Studies of the Lattice Vacancy and Low Temperature Damage Processes in Silicon,” Lattice Defects in Semiconductors
1974, Huntley ed., 1975, Inst. Phys. Conf. Ser. 23, London.
G.A. Baraff and M. Schluter, “Electronic Structure, Total Energies, and
Abundances of the Elementary Point Defects in GaAs,” Phys. Rev.
Lett., 55, 1327 (1985).
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, magnesium, phosphorus, selenium, isilicon, tin, and zinc
statements.
220
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ZINC
COMMAND
ZINC
Set the coefficients of zinc kinetics.
SYNOPSIS
zinc
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0=<n> ] [ Dix.E=<n> ]
[ Dip.0=<n> ] [ Dip.E=<n> ] [ Dipp.0=<n> ] [ Dipp.E=<n> ]
[ Fi = <n> ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp=<n> ] [ ss.conc=<n> ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly |
/gaas ) ]
[ Seg.0=<n> ] [ Seg.E=<n> ] [ Trn.0=<n> ] [ Trn.E=<n> ]
[ ( donor | acceptor ) ]
DESCRIPTION
This statement allows the user to specify values for coefficients of zinc
diffusion and segregation. The diffusion equation for zinc is:
∂C T
∂t
= ∇ DV CA
CV
*
CV
CV p
CI
CI p
∇ln C A *  + D I C A * ∇ln C A * 
 CV ni 
 CI ni 
CI
(EQ 75)
where CT and CA are the total chemical and active concentrations of zinc,
CA is the total electrically active concentration of zinc, CV and CI are the
vacancy and interstitial concentrations, the superscript * refers to the equi-
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
221
ZINC
librium value, DV and DI are the diffusivities with vacancies and interstitials, and p and ni refer to the hole concentration and the intrinsic electron
concentration respectively. The diffusivities are given by:
p
p 2

D V = ( 1 − F i ) D X + D p ( ) + D PP ( )

ni
ni 
(EQ 76)
p
p 2

D I = F i D X + D p ( ) + D PP ( )

ni
ni 
(EQ 77)
DX , DP , and DPP are described in greater detail below.
The segregation at material interfaces is computed using the following expression:
C2 

flux = T r C 1
 M 12 
(EQ 78)
where C1 and C2 are the concentrations in material 1 and 2 respectively,
and the M12 and Tr terms are computed using expressions shown below
with the parameters of the models.
silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of
these can be specified per statement. The parameters specified in that
statement will apply in the material listed. These parameters specify which
material is material 1 for the segregation terms.
Dix.0, Dix.E
These floating point parameters allow the specification of DX , the zinc diffusivity with neutral defects. Dix.0 is the pre-exponential constant and
Dix.E is the activation energy. Dix.0 defaults to 0.0 cm2/sec in gallium ars-
222
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ZINC
enide, and Dix.E defaults to 0.0 eV in gallium arsenide. DX is calculated
using a standard Arrhenius relationship.
Dip.0, Dip.E
These floating point parameters allow the specification of DP, the beryllium diffusivity with singly positive defects. Dip.0 is the pre-exponential
constant and Dip.E is the activation energy. Dip.0 defaults to 0.0 cm2/sec
in gallium arsenide, and Dip.E defaults to 0.0 eV in gallium arsenide. DP is
calculated using a standard Arrhenius relationship.
Dipp.0, Dipp.E
These floating point parameters allow the specification of DPP, the zinc
diffusivity with doubly positive defects. Dipp.0 is the pre-exponential constant and Dipp.E is the activation energy. Dipp.0 defaults to 1.2×102 cm2/
sec for implanted zinc in gallium arsenide and 15.6 cm2/sec for grown-in
zinc in gallium arsenide, and Dipp.E defaults to 3.9 eV for both in gallium
arsenide[1,2]. DPP is calculated using a standard Arrhenius relationship.
Fi
This parameter allows the specification of the fractional interstitialcy. This
value indicates whether zinc diffuses through interaction with interstitials
or vacancies. The value of Fi defaults to 1.0.
implanted, grown.in
Specifies whether the Dix, Dip, Dipp, or Fi coefficients apply to implanted
or grown-in zinc. If neither is specified then a specified parameter applies
to both.
ss.clear
This parameter clears the currently stored solid solubility data.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
223
ZINC
ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration
point to those already stored. The default values are:
ss.temp
ss.conc
700˚C
1.0×1019 cm-3
1250˚C
1.0×1019 cm-3
/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can
be specified at one time.
Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation
concentrations. The segregation constant follows an Arrhenius relationship.
Trn.0, Trn.E
These parameters allow the specification of the transport velocity across
the interface given. The units are in cm/sec. The transfer coefficient follows an Arrhenius relationship.
donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are
not presently material specific. By default, zinc is an acceptor.
224
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
ZINC
EXAMPLES
zinc gaas implanted Dip.0=2.2e-6 Dip.E=1.76
This command changes the positive defect diffusivity for implanted zinc
in gallium arsenide.
zinc gaas /nitride Seg.0=1126.0 Seg.E=0.91 Trn.0=1.66e-7
This command will change the segregation parameters at the gallium arsenide – silicon nitride interface. The gallium arsenide concentration will
be half the nitride concentration in equilibrium at 1100˚C.
BUGS
As far as the implemented models are physically correct, there are no
known bugs.
REFERENCES
1. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1990.
2. J.D. Plummer et al., “Process Simulators for Si VLSI and High Speed
GaAs Devices,” Stanford University Technical Report, 1991.
SEE ALSO
The antimony, arsenic, beryllium, boron, carbon, generic, germanium,
interstitial, magnesium, phosphorus, selenium, isilicon, tin, and vacancy statements.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
225
ZINC
226
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
Examples
INTRODUCTION
This section contains several examples showing the use of
SUPREM-IV.GS. The first nine examples are from the pre-gallium arsenide version of the program and show silicon processing exclusively.
However, these examples are still useful for users interested in GaAs processing as they exploit many of the program’s features that are common to
all aspects of semiconductor process simulation. The remaining examples
concentrate on GaAs process simulation. Only those commands that are
unique to GaAs simulation are discussed.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
227
Examples
228
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 1: Boron Anneal – 1D
EXAMPLE 1
Boron Anneal – 1D
DESCRIPTION
This example performs a simple anneal of a boron implant. The final
structure is saved, and then various post processing is performed. The input file for the simulation is in the “examples/exam1” directory, in the file
boron.in.
#some set stuff
set echo
option quiet
mode one.dim
#the
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 0.50 spacing = 0.02
x loc = 2.0
spacing = 0.25 tag=bottom
#the silicon wafer
region silicon xlo = top xhi = bottom
#set up the exposed surfaces
bound exposed xlo = top xhi = top
#calculate the mesh
init boron conc=1.0e14
#the pad oxide
deposit oxide thick=0.075
#the uniform boron implant
implant boron dose=3e14 energy=70 pearson
#plot the initial profile
select z=log10(boron)
plot.1d x.max=2.0 y.min=14.0 y.max=20.0
#the diffusion card
diffuse time=30 temp=1100
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
229
EXAMPLE 1: Boron Anneal – 1D
#save the data
structure out=boron.str
#plot the final profile
select z=log10(bor)
plot.1d x.max=2.0 cle=f axi=f
The first lines in the input deck set some basic SUPREM-IV.GS options.
#some set stuff
set echo
option quiet
mode one.dim
The '#' character is the comment character for SUPREM-IV.GS. The entire
line after the '#' is ignored. The echo flag is turned on. This instructs
SUPREM-IV.GS to echo input lines after they are typed. This is useful
when the output from the simulator is being redirected into a file, so the
commands are in the output listing. The second command instructs the
simulator to be quiet about what it is doing. The default option is verbose,
but this prints far more information than is needed by the novice user. The
final command specifies that the simulation will be done in one dimension.
It is therefore necessary to specify only vertical grid information.
The next section begins the definition of the mesh to be used for the simulation. The section
#the
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 0.50 spacing = 0.02
x loc = 2.0
spacing = 0.25 tag=bottom
describes the locations of the x lines in the mesh. SUPREM-IV.GS, in one
dimensional mode, defines x to be the direction into the wafer. In two-dimensional mode, x is across the wafer top and y is the direction into the
wafer. This simulation is to be done on a one dimensional problem, therefore lines are only specified in the x direction. The first statement places a
230
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 1: Boron Anneal – 1D
mesh line at the top of wafer, x coordinate 0.0µm and tags the line as
“top”. The spacing is set to 0.02µm. A line is placed at 0.5µm which is the
expected starting depth of the implanted profile. The spacing is set to
0.02µm. Since the spacing between the first two mesh lines is the same,
0.02µm, there will be mesh lines placed 0.02µm apart between 0.0 and
0.50µm. Finally a line is placed at 2.0µm, which is greater than the depth
of the profile after the anneal. The spacing here is set to 0.25µm. In the
case where spacings are different in neighboring lines, the spacing is graded between them. The distance between mesh lines near 0.5µm will be
0.02µm and the distance will get progressively closer to 0.25µm as the
mesh gets closer to 2.0µm. The line statement fixes line locations in the
mesh as well as the average spacing between lines.
The next two sections describe the device starting material and the surfaces which are exposed to gas.
#the silicon wafer
region silicon xlo = top xhi = bottom
#set up the exposed surfaces
bound exposed xlo = top xhi = top
The region statement is used to define the starting materials. In this case
the wafer is silicon with no initial masking layers. The silicon area is defined to extend between the lines tagged top and bottom in the vertical direction. Looking back at the mesh line definition section, this corresponds
to the entire area that had been defined. The initial simulation area is completely silicon.
The bound statement allows the definition of the front and backsides of the
wafer. Any gases on the diffuse, deposit, and etch statements are applied
to the surface marked exposed. It is important to define the top of the wafer for SUPREM-IV.GS to correctly simulate these actions. Most mistakes
are made by ignoring to define the exposed surface.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
231
EXAMPLE 1: Boron Anneal – 1D
The next line informs SUPREM-IV.GS that the mesh has been defined and
should be computed.
#calculate the mesh
init boron conc=1.0e14
This statement computes the locations of lines given the spacings, triangulates the rectangular mesh, and computes geometry information. The initial doping is boron with a concentration of 1×1014 cm-3.
The next line adds a pad oxide to the wafer.
#the pad oxide
deposit oxide thick=0.075
The deposited oxide is specified to 0.075µm thick. This represents the pad
oxide that is grown before the uniform boron implant. Rather than simulate the growth, it is simpler to add a deposited oxide the correct thickness
of the pad.
The next statement performs the implant of the boron.
#the uniform boron implant
implant boron dose=3e14 energy=70 pearson
The implant is modeled with a Pearson-IV distribution. The energy and
dose are 3×1014 cm-2 and 70KeV respectively. This produces an abrupt
boron profile with a junction near 0.3µm.
The next commands choose a plot variable and display it.
#plot the initial profile
select z=log10(boron)
plot.1d x.max=2.0 y.min=14.0 y.max=20.0
The plot will look like Figure 1. The select statement selects the plot variable to be the log base ten of the boron concentration. The plot.1d statement does not need to specify the location of the cross section in one
232
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 1: Boron Anneal – 1D
dimension. The plot should extend between the minimum value of y
through 2.0µm. Dimensions on the plot command always refer to the plot
axis. In this case, the x axis is the depth dimension, and the y axis is the
log of the boron concentration. The minimum and maximum on the y axis
are set to 1014 and 10 20. The y axis values have to be specified in the units
of the selected variable, log10 of concentration.
FIGURE 1
Implanted Boron profile.
The diffuse command simulates the 30 minute, 1100˚C anneal.
#the diffusion card
diffuse time=30 temp=1100
The default ambient is inert, so no oxide will be grown. The diffuse command will produce the following output:
estimated first time step -0.000000e+00
Solving
0 +
0.1 =
0.1,
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
100%, np 43
233
EXAMPLE 1: Boron Anneal – 1D
Solving
0.1
Solving 0.588986
Solving 3.50548
Solving 8.86554
Solving 17.4079
Solving 21.2092
Solving 34.0042
Solving 49.4183
Solving 71.6822
Solving 99.699
Solving 126.191
Solving 167.318
Solving 196.947
Solving 253.434
Solving 313.837
Solving 405.867
Solving 509.654
Solving 583.334
Solving 758.821
Solving 963.93
Solving 1229.64
Solving 1606.02
+ 0.488986 =
+
2.9165 =
+ 5.36005 =
+ 8.54232 =
+ 3.80138 =
+
12.795 =
+ 15.4141 =
+ 22.2639 =
+ 28.0168 =
+ 26.4923 =
+ 41.1269 =
+
29.629 =
+ 56.4872 =
+ 60.4027 =
+ 92.0295 =
+ 103.787 =
+ 73.6803 =
+ 175.487 =
+ 205.108 =
+
265.71 =
+ 376.381 =
+ 193.979 =
0.588986,
3.50548,
8.86554,
17.4079,
21.2092,
34.0042,
49.4183,
71.6822,
99.699,
126.191,
167.318,
196.947,
253.434,
313.837,
405.867,
509.654,
583.334,
758.821,
963.93,
1229.64,
1606.02,
1800,
488.986%,
596.438%,
183.784%,
159.37%,
44.5005%,
336.588%,
120.47%,
144.439%,
125.839%,
94.5586%,
155.241%,
72.0429%,
190.649%,
106.932%,
152.36%,
112.776%,
70.9916%,
238.174%,
116.879%,
129.546%,
141.651%,
51.5381%,
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
43
The first line prints the estimate of the initial time step size. The message
is informative only. Each of the following lines indicates a time step of the
diffusion. The format is the current time + the size of the time step will
equal the time after the step. The user can, therefore, determine exactly
how far the simulation has proceeded. The next number is the size of the
next time step, expressed as a percentage of the current time step. It can be
seen for this problem that the time step increases regularly. The final bit of
information is the number of points in the mesh, 43 in this example.
The next step is to save the data for further examination.
#save the data
structure out=boron.str
This saves the data in the file boron.str. This file can be read in using the
init command or the structure command.
234
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 1: Boron Anneal – 1D
The following script will plot the final boron concentration.
#plot the final profile
select z=log10(bor)
plot.1d x.max=2.0 cle=f axi=f
The first statement picks the log base ten of the boron concentration to
plot. The plot will be placed on the earlier plot. The “cle=f axi=f” instructs
SUPREM-IV.GS to not clear and not compute new axes.
Figure 2 shows a deeper junction as expected, as well as segregation into
the oxide. The spike at the surface indicates that the surface oxide concentration is about 20 times larger than the silicon surface concentration.
FIGURE 2
Comparison of annealed and implanted boron profiles.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
235
EXAMPLE 1: Boron Anneal – 1D
236
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 2: Boron OED – 1D
EXAMPLE 2
Boron OED – 1D
DESCRIPTION
This example performs a simple anneal of a boron implant under a dry oxygen ambient. The interstitials are injected by the growing oxide and will
enhance the boron diffusivity. This example will produce a deeper boron
junction than Example 1 because of the interstitial injection. The final
structure is saved, and then various post processing is performed. The input file for the simulation is in the “examples/exam2” directory, in the file
oed.in.
#some set stuff
set echo
option quiet
mode one.dim
#the
line
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 1.50 spacing = 0.05
x loc = 5.0
spacing = 0.5
x loc = 400.0
tag=bottom
#the silicon wafer
region silicon xlo = top xhi = bottom
#set up the exposed surfaces
bound exposed xlo = top xhi = top
#calculate the mesh
init boron conc=1.0e14
#the pad oxide
deposit oxide thick=0.075
#the uniform boron implant
implant boron dose=3e14 energy=70 pearson
#plot the initial profile
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
237
EXAMPLE 2: Boron OED – 1D
select z=log10(boron)
plot.1d x.ma=2.0 y.mi=14.0 y.max=20.0
#the diffusion card
method init=1.0e-3 two.d
diffuse time=30 temp=1100 dry
#save the data
structure out=oed.str
#plot the final profile
select z=log10(bor)
plot.1d cle=f axi=f
This example is very similar to Example 1. It starts by setting command
line echoing and by instructing SUPREM-IV.GS to be relatively quiet
about the progress of computation. The y line section is considerably different. In this example, we wish to calculate the oxidation enhanced diffusion of a boron layer under a growing oxide. Therefore, the vertical
specification needs to be different.
#the
line
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 1.50 spacing = 0.05
x loc = 5.0
spacing = 0.5
x loc = 400.0
tag=bottom
This is similar to the first example. However, we expect the junction to be
deeper, therefore the tight grid spacing is maintained out to 1.5µm. The
spacing is increased out to a depth of 5µm. The backside is placed at the
full thickness of the wafer since the defects can travel great distances into
the silicon substrate.
The next series of lines define the region, boundary, and initialize the wafer. A starting oxide is deposited and the boron implant is performed.
These steps are all identical to Example 1.
238
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 2: Boron OED – 1D
The next set of commands choose a plot variable and display it. This plot
will be identical to Figure 1 of Example 1.
The diffuse command contains the directive to simulate the 30 minute,
1100˚C drive-in and anneal.
#the diffusion card
method two.d init=1.0e-3
diffuse time=30 temp=1100 dry
The ambient is dry oxygen. The diffuse command will produce the following output:
estimated first time step -0.000000e+00
Solving
0 +
0.001 =
0.001,
100%,
Solving
0.001 +0.0028164 =0.0038164,281.644%,
Solving0.0038164 +0.0176591 =0.0214756,627.002%,
Solving0.0214756 + 0.168429 = 0.189905,953.779%,
Solving 0.189905 + 0.813906 = 1.00381,483.233%,
Solving 1.00381 +
2.6438 = 3.64761,324.828%,
Solving 3.64761 + 6.03434 = 9.68195,228.245%,
Solving 9.68195 + 9.78821 = 19.4702,162.208%,
Solving 19.4702 + 14.1452 = 33.6153,144.512%,
Solving 33.6153 + 19.4714 = 53.0868,137.654%,
Solving 53.0868 + 26.1378 = 79.2245,134.236%,
Solving 79.2245 + 35.1156 =
114.34,134.348%,
Solving
114.34 + 38.3539 = 152.694,109.222%,
Solving 152.694 + 44.1769 = 196.871,115.182%,
Solving 196.871 + 63.5629 = 260.434,143.883%,
Solving 260.434 + 84.4433 = 344.877, 132.85%,
Solving 344.877 +
105.6 = 450.477,125.054%,
Solving 450.477 + 78.7206 = 529.198, 74.546%,
Solving 529.198 + 71.7795 = 600.977,91.1826%,
Solving 600.977 + 121.337 = 722.315,169.042%,
Solving 722.315 +
191.01 = 913.324, 157.42%,
Solving 913.324 + 108.262 = 1021.59,56.6788%,
Solving 1021.59 + 193.111 =
1214.7,178.374%,
Solving
1214.7 + 350.262 = 1564.96,181.378%,
Solving 1564.96 + 235.041 =
1800,67.1044%,
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
np
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
80
81
The first thing to notice, in comparison to Example 1, is that more time
steps are needed. This is for two reasons. First, the defects move faster
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
239
EXAMPLE 2: Boron OED – 1D
than the boron and they limit the size of the time step initially. At longer
times, the defects begin to approach steady state, and the boron diffusion
limits the time step. Since the boron diffusivity is enhanced by the injection of interstitials, the time steps have to be smaller than in Example 1 to
resolve the faster changes in the boron.
The next step is to save the data for further examination.
#save the data
structure out=boron.str
This saves the data in the file boron.str. This file can be read in using the
initialize command or the structure command.
The following script will plot the final boron concentration.
#plot the final profile
select z=log10(bor)
plot.1d cle=f axi=f
The first command picks the log base ten of the boron concentration to
plot. The plot will be placed on the earlier plot. The “cle=f axi=f” instructs
SUPREM-IV.GS to not clear and not compute new axes.
The profile in Figure 1 shows a deeper junction as expected, as well as
segregation into the oxide. The spike at the surface indicates that the surface oxide concentration is about 20 times larger than the silicon surface
concentration.
240
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 2: Boron OED – 1D
FIGURE 1
Final structure comparing the boron before and after anneal.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
241
EXAMPLE 2: Boron OED – 1D
242
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 3: OED Time
EXAMPLE 3
OED Time
DESCRIPTION
This example uses the movie command to look at the time dependence of
the interstitial concentration resulting from oxide growth. This simulation
will be of a silicon membrane 28 µm thick. This will allow the simulation
of the effective diffusivity. The input file for the simulation is in the “examples/exam3” directory, in the file oed.in.
#some set stuff
option quiet
mode one.dim
#the
line
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 1.50 spacing = 0.05
x loc = 5.0
spacing = 0.5
x loc = 28.0 tag=bottom
#the silicon wafer
region silicon xlo = top xhi = bottom
#set up the exposed surfaces
bound exposed xlo = top xhi = top
bound backsid xlo = bottom xhi = bottom
#calculate the mesh
init
#the pad oxide
deposit oxide thick=0.02
#the diffusion card
method init=1.0e-3 two.d
#set up some integration variables
%define otim 0.0
%define oldfci 1.0
%define oldbci 1.0
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
243
EXAMPLE 3: OED Time
%define tfci 0.0
%define tbci 0.0
%diffuse time=240 temp=1100 dry movie="
select z=(inter/ci.star);
%define newfci zfn(0.0,sil@oxi(0.0)+1.0e-6)
%define newbci zfn(0.0,27.9)
%define tfci ${tfci}+0.5*(${time}-${otim})*(${newfci}+${oldfci})
%define tbci ${tbci}+0.5*(${time}-${otim})*(${newbci}+${oldbci})
%define den ${time}+1.0e-6
printf Data ${time}/60.0 (${tfci}/${den})
(${tbci}/${den})
%define otim ${time}
%define oldfci ${newfci}
%define oldbci ${newbci}"
#save the data
structure out=oed.str
This example is very similar to Example 2. It starts by instructing
SUPREM-IV.GS to be relatively quiet about the progress of computation.
The y line section is somewhat different. In this example, we wish to calculate the oxidation enhanced diffusion resulting from a growing oxide.
Therefore, the vertical specification needs to be different.
#the
line
line
line
line
vertical definition
x loc = 0
spacing = 0.02 tag = top
x loc = 1.50 spacing = 0.05
x loc = 5.0
spacing = 0.5
x loc = 28.0 tag=bottom
This is similar to the last example. The backside is placed at the membrane
thickness so that we can compute the interstitials at this interface.
The next series of commands define the region, boundary, and initialize
the wafer. The are only two differences between this example and the
previous one. First is the specification of a backside interface. This will allow the specification of boundary conditions for the defects. Second, no
244
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 3: OED Time
boron implant is performed. This will speed the simulation. A starting oxide is deposited next. The method command specifies the defects should
be solved and sets a small initial time step.
The next set of commands initialize some variables that will be used in the
diffuse statement.
#set up
%define
%define
%define
%define
%define
some integration variables
otim 0.0
oldfci 1.0
oldbci 1.0
tfci 0.0
tbci 0.0
In this diffusion, the time average value of the interstitial concentration
will be calculated and printed. The variable otim is the old time, oldcfi is
the old scaled interstitial concentration at the front, oldbci is the old interstitial concentration at the back, and tfci and tbci are the time averaged
values of the scaled interstitial concentration at the front and back respectively.
The diffuse command contains the directive to simulate the 30 minute,
1100˚C, dry oxygen drive in and anneal.
#the diffusion card
%diffuse time=30 temp=1100 dry movie="
In this example, the movie parameter is used to compute the time average
of the interstitial concentration at the front and backside. The entire quoted
string for the movie parameter is treated as SUPREM-IV.GS input at the
end of every time step. This allows a time history to be developed.
select z=(inter/ci.star);
%define newfci zfn(0.0,sil@oxi(0.0)+1.0e-6)
%define newbci zfn(0.0,27.99)
%define tfci ${tfci}+0.5*(${time}-${otim})*(${newfci}+${oldfci})
%define tbci ${tbci}+0.5*(${time}-${otim})*(${newbci}+${oldbci})
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
245
EXAMPLE 3: OED Time
%define den ${time}+1.0e-6
printf Data ${time}/60.0 (${tfci}/${den})
(${tbci}/${den})
%define otim ${time}
%define oldfci ${newfci}
%define oldbci ${newbci}"
The first command in the movie line is to select the scaled interstitial concentration, CI / CI* as the plot variable. The next line defines the variable
newfci to be equal to the value of the z value interpolated at x = 0.0µm
and y = 1Å below the silicon / silicon dioxide interface. This effectively is
the surface value of the scaled interstitial concentration. The next line sets
newbci to the back side interstitial concentration. The integrated time value at the front and back sides are computed and assigned to the variables
totfci and totbci. This time integration uses the trapezoidal rule to compute the values. The time is adjusted by one microsecond in the computation of the average to avoid divide by zero errors. The printf command
prints the current time in the diffusion and the front and back side time averaged values. Finally, the variables representing the previous time step
values are updated.
The diffuse command should produce output of the form:
estimated first time step 8.740542e-10
Data 0 0 0
Solving
0 +
0.001 =
0.001,
100%,
Data 1.66667e-05 1.14116 0.999001
Solving
0.001 +0.0021718 =0.0031718,217.181%,
Data 5.28635e-05 1.23489 0.999685
Solving0.0031718 +0.0105442 = 0.013716,485.503%,
Data 0.0002286 1.26412 0.999927
Solving 0.013716 +0.0857607 =0.0994767,813.344%,
Data 0.00165794 1.27887 0.99999
Solving0.0994767 + 0.380333 = 0.47981,443.482%,
Data 0.00799683 1.31034 0.999998
Solving 0.47981 + 1.11267 = 1.59248,292.553%,
Data 0.0265413 1.39119 1
Solving 1.59248 + 2.71156 = 4.30404,243.697%,
Data 0.071734 1.5448 1
246
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
np 73
np 73
np 73
np 73
np 73
np 73
np 73
EXAMPLE 3: OED Time
Solving 4.30404 + 7.50309 =
Data 0.196785 1.81401 1
Solving 11.8071 + 23.0711 =
Data 0.581303 2.21682 1
Solving 34.8782 + 52.5225 =
Data 1.45668 2.59747 1
Solving 87.4007 + 116.309 =
Data 3.39517 2.8976 1
Solving
203.71 + 264.827 =
Data 7.80895 3.09822 1.00005
Solving 468.537 + 629.713 =
Data 18.3042 3.19492 1.00143
Solving 1098.25 + 1476.13 =
Data 42.9063 3.19724 1.02452
Solving 2574.38 + 1786.28 =
Data 72.6777 3.13466 1.09187
Solving 4360.66 + 2319.41 =
Data 94.745 3.07212 1.16452
Solving
5684.7 + 2813.18 =
Data 141.631 2.96848 1.34316
Solving 8497.88 + 3114.92 =
Data 193.547 2.89165 1.53193
Solving 11612.8 + 2787.21 =
Data 240 2.83454 1.67415
11.8071,276.707%, np 73
34.8782,307.488%, np 73
87.4007,227.655%, np 73
203.71,221.446%, np 73
468.537,227.693%, np 73
1098.25,237.783%, np 73
2574.38,234.413%, np 72
4360.66,121.011%, np 71
6680.07,129.846%, np 71
8497.88,212.469%, np 71
11612.8,110.726%, np 70
14400,89.4793%, np 69
The lines starting Data show the time in minutes and the front and back
side time averaged interstitial concentration. The interstitial concentration
ramps up and then levels off. As the simulation continues, the interstitial
concentration falls off due to the decreased oxidation rate. The output can
be redirected to a file and then plotted using any number of x-y plot programs.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
247
EXAMPLE 3: OED Time
248
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 4: Boron OED – 2D
EXAMPLE 4
Boron OED – 2D
DESCRIPTION
This example performs a simple anneal of a boron implant under a dry oxygen ambient. The interstitials are injected by the growing oxide and will
enhance the boron diffusivity. This example will use a two dimensional
structure to investigate the lateral extent of the oxidation enhanced diffusion behavior. In addition, the two dimensional growth of the oxide will be
simulated. The final structure is saved, and then various post processing is
performed. The input file for the simulation is in the "examples/exam4" directory, in the file oed.in.
#some set stuff
set echo
#the
line
line
line
x
x
x
x
dimension definition
loc = -2.0 tag = left
loc = 0.0 spacing=0.05
loc = 5.0 tag = right
#the
line
line
line
vertical definition
y loc = 0
spacing = 0.02 tag = top
y loc = 1.5
spacing = 0.05
y loc = 400.0
tag=bottom
#the silicon wafer
region silicon xlo = left xhi = right ylo = top yhi =
bottom
#set up the exposed surfaces
bound exposed xlo = left xhi = right ylo = top
top
yhi =
#calculate the mesh
init boron conc=1.0e14
#the pad oxide
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
249
EXAMPLE 4: Boron OED – 2D
deposit oxide thick=0.02
#deposit the nitride mask
deposit nitride thick=0.05
etch nitride right p1.x=0.0 p2.x=0.0
#the boron implant
implant boron dose=3e14 energy=40 pearson
#the diffusion card
method two.d
diffuse time=30 temp=1100 dry
#save the data
structure out=oed.str
This example is very similar to Example 2. It starts by setting command
line echoing and by instructing SUPREM-IV.GS to be relatively quiet
about the progress of computation. The x line specification is different for
the two dimensional device. For this example, an x line is placed at -2µm
and another at 5µm for the left and right of the device. The area of most
interest is the middle area near where the mask edge will be placed. Consequently, a tighter spacing is specified at the mask edge.
The next series of lines define the y lines, region, boundary, and initialize
the wafer. A starting oxide is deposited and the boron implant is performed. These steps are all similar to Example 2.
Following the boron implant, a mask is deposited and etched.
#deposit the nitride mask
deposit nitride thick=0.05
etch nitride right p1.x=0.0 p2.x=0.0
The mask material is specified to be 0.05 µm of nitride. This will mask the
oxide growth. The nitride is etched off to the right of a vertical line at x
equal to 0µm. The oxide will grow on the right and inject interstitials
there.
250
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 4: Boron OED – 2D
The diffuse command contains the directive to simulate the 30 minute,
1100˚C drive-in and anneal.
#the diffusion card
method two.d init=1.0e-3
diffuse time=30 temp=1100 dry
The ambient is dry oxygen. This diffusion step will produce output similar
to Example 2.
The next step is to save the data for further examination.
#save the data
structure out=oed.str
This saves the data in the file oed.str. This file can be read in using the init
command or the structure command.
The following commands are not in an input deck, instead type them in to
the simulator using the interactive facilities to plot and check data. The
first command will be to read in the stored structure file. Type:
init inf=oed.str
This will read in the file and initialize the data structures of the program.
The final lines will plot the final boron concentration, in two dimensions
#plot the final profile
select z=log10(bor)
plot.2d bound fill y.max=2.0
foreach v (15.0 to 19.0 step 0.5)
contour val=v
end
The first statement picks the log base ten of the boron concentration to
plot. The next statement instructs SUPREM-IV.GS to plot the two dimensional outline of the device. The bound parameter asks for the material
boundaries to be plotted. The area plotted will extend only down to y
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
251
EXAMPLE 4: Boron OED – 2D
equal to 2µm. The contour statements are plotted as part of loop. The
foreach command repeats 9 times and sets the variable v to the value
specified in the loop. Figure 1 shows that the lateral extent of the OED is
well over two microns. There is little lateral difference in the shape of the
profile.
FIGURE 1
Boron contours resulting from the implant and anneal.
The interstitial concentration can also be plotted. This will verify that
there is little lateral decay in the defect profile.
#plot the final profile
select z=(inter/ci.star)
plot.2d bound fill y.max=10.0
foreach v (1.25 to 3.0 step 0.25)
contour val=v
end
252
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 4: Boron OED – 2D
Figure 2 shows the result. There is more shape to the defects than the boron. However, the profile is fairly flat across the top of the wafer.
FIGURE 2
Interstitial contours resulting from the injection.
The interstitial concentration can also be plotted in cross section and is
shown in Figure 3.
plot.1d y.v=0.5
This command will plot the interstitial concentration 0.5µm below the surface.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
253
EXAMPLE 4: Boron OED – 2D
FIGURE 3
Lateral cross section of the interstitial profile.
The value can also be plotted vertically, and is shown in Figure 4.
plot.1d x.v=5.0 x.ma=75.0
This shows the penetration into the bulk of the interstitials. The penetration is limited by both the bulk recombination of the interstitials with vacancies and the trapping mechanism.
254
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 4: Boron OED – 2D
FIGURE 4
Vertical cross section of the interstitial profile.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
255
EXAMPLE 4: Boron OED – 2D
256
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 5: LDD Cross Section
EXAMPLE 5
LDD Cross Section
DESCRIPTION
This example simulates the anneal of a lightly doped drain cross section.
This example will produce a cross section appropriate to pass to
PISCES-II for device simulation. This example is in the directory “example/exam5”, and the file whole.s4.
set echo
cpu log
phos poly /gas Trn.0=0.0
bor poly /gas Trn.0=0.0
phos oxide /gas Trn.0=0.0
bor oxide /gas Trn.0=0.0
line
line
line
line
line
x
x
x
x
x
loc=0.0 tag=lft
loc=0.45
loc=0.75
loc=1.4
loc=1.5 tag=rht
spacing=0.25
spacing=0.03
spacing=0.03
spacing=0.25
spacing=0.25
line
line
line
line
y
y
y
y
loc=0.0 tag=top spacing=0.01
loc=0.1
spacing=0.01
loc=0.25
spacing=0.05
loc=3.0 tag=bot
region silicon xlo=lft xhi=rht ylo=top yhi=bot
bound exposed xlo=lft xhi=rht ylo=top yhi=top
bound backside xlo=lft xhi=rht ylo=bot yhi=bot
init boron conc=1.0e16
#deposit the gate oxide
deposit oxide thick=0.025
#channel implant
implant boron dose=1.0e12 energy=15.0
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
257
EXAMPLE 5: LDD Cross Section
#deposit the gate poly
deposit poly thick=0.500 div=10 phos conc=1.0e19
#anneal
diff time=10 temp=1000
#etch the poly away
etch poly right p1.x=0.55 p1.y=-0.020 p2.x=0.45 p2.y=0.55
#anneal this step
diffuse time=30.0 temp=950
struct outf=poly.str
#do the phosphorus implant
implant phos dose=1.0e13 energy=50.0
#deposit the oxide spacer
deposit oxide thick=0.400 spac=0.05
#etch the spacer back
etch dry oxide thick=0.420
struct outf=imp2.str
#after etch anneal
method vert fermi grid.ox=0.0
diffuse time=30 temp=950 dry
#implant the arsenic
implant ars dose=5.0e15 energy=80.0
#deposit a cap oxide
deposit oxide thick=0.15 space=0.03
struct outf=imp4.str
#do the final anneal
diffuse time=20 temp=950
struct outf=ldd.str
258
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 5: LDD Cross Section
The next section begins the definition of the mesh to be used for the simulation. The section
phos poly /gas Trn.0=0.0
bor poly /gas Trn.0=0.0
phos oxide /gas Trn.0=0.0
bor oxide /gas Trn.0=0.0
turns off the out diffusion of phosphorus and boron. In this simulation,
there are anneals of bare poly. To keep the time step from being limited by
the out-diffusion behavior, the gas transport is turned off by setting the
transport rate pre-exponential constant to zero.
The next section describes the locations of the x lines in the mesh.
line
line
line
line
line
x
x
x
x
x
loc=0.0 tag=lft
loc=0.45
loc=0.75
loc=1.4
loc=1.5 tag=rht
spacing=0.25
spacing=0.03
spacing=0.03
spacing=0.25
spacing=0.25
SUPREM-IV.GS defines x to be the direction across the top of the wafer,
and y to be the vertical dimension into the wafer. Similar to Example 4,
the location of the mesh lines is chosen to minimize the spatial error and to
represent the location of various etch steps.
The next section of input describes the location and spacings of the vertical mesh lines.
line
line
line
line
y
y
y
y
loc=0.0 tag=top spacing=0.01
loc=0.1
spacing=0.01
loc=0.25
spacing=0.05
loc=3.0 tag=bot
The lines are chosen close together near the surface and increasing away
from it. Tight spacing is maintained only near the top surface. Since the
structure will be passed to PISCES-II, a depth of 3.0µm is chosen so that
the eventual substrate contact will be deep to not unduly influence the simulation.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
259
EXAMPLE 5: LDD Cross Section
The next two sections describe the device starting material and the surfaces which are exposed to gas.
region silicon xlo=lft xhi=rht ylo=top yhi=bot
bound exposed xlo=lft xhi=rht ylo=top yhi=top
bound backside xlo=lft xhi=rht ylo=bot yhi=bot
The region statement is used to define the starting materials. In this case
the wafer is silicon with no initial masking layers. The bound statement
allows the definition of the front and backsides of the wafer. Any gasses
on the diffuse, deposit, and etch commands are applied to the surface
marked exposed. The backside will not influence the process simulation.
However, the backside is the location of a contact when the specfication of
the electrodes is made for PISCES-II.
The next line informs SUPREM-IV.GS that the mesh has been defined and
should be computed.
init boron conc=1.0e16
#deposit the gate oxide
deposit oxide thick=0.025
The first line initializes the starting material. The deposited oxide is specified to 0.025µm thick. This represents the gate oxide that is grown before
the uniform boron implant.
The next statement performs the channel implant of the boron.
#channel implant
implant boron dose=1.0e12 energy=15.0
The implant is modeled with a Pearson-IV distribution. The energy and
dose are 1012 cm-2 and 15KeV respectively. This produces an abrupt boron profile with a shallow junction.
260
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 5: LDD Cross Section
The next commands define the poly deposition and anneal. The poly deposition is done first, then the heat cycle that follows does the temperature
cycle that occurs during actual poly deposition.
#deposit the gate poly
deposit poly thick=0.500 div=10 phos conc=1.0e19
#anneal
diff time=10 temp=1000
#etch the poly away
etch poly right p1.x=0.55 p1.y=-0.020 p2.x=0.45 p2.y=0.55
#anneal this step
diffuse time=30.0 temp=950
struct outf=poly.str
The first pair of statements deposit the poly and then provide a temperature step representing the deposition. This temperature step will cause diffusion of the threshold adjust implant. The poly is put down with ten grid
layers and doped to concentration of 1019 cm-3 phosphorus. The next statements etch the gate material and perform a poly anneal. The structure is
then saved in the file “poly.str”.
The phosphorus light implant and spacer definition comes next.
#do the phosphorus implant
implant phos dose=1.0e13 energy=50.0
#deposit the oxide spacer
deposit oxide thick=0.400 spac=0.05
#etch the spacer back
etch dry oxide thick=0.420
struct outf=imp2.str
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
261
EXAMPLE 5: LDD Cross Section
This implant is the one which will form the lightly doped drain. The next
two steps of the full device are to deposit and etch the spacer oxide. The
spacer is deposited with 10 divisions, and the curvature is resolved to
0.04µm. The oxide is etched back a thickness of 0.42µm. The dry parameter indicates that the oxide surface is to be dropped straight down. Finally, the structure at this stage is saved.
The oxide is regrown and the phosphorus annealed during the next step.
#after etch anneal
method vert fermi grid.ox=0.0
diffuse time=30 temp=950 dry
The method command specifies the oxide will grow vertically. No injection of interstitials will be simulated during this oxide growth. The diffuse
command specifies that the anneal is to be done for 30 minutes at 950˚C in
dry O2.
The next step implants the heavily doped portion of the drain, and deposits
the cap oxide.
#implant the arsenic
implant ars dose=5.0e15 energy=80.0
#deposit a cap oxide
deposit oxide thick=0.15 space=0.03
struct outf=imp4.str
The arsenic is implanted through the new oxide growth and then a cap oxide is deposited. The structure is saved in the file “imp4.str”.
Finally, we want to do the final anneal.
#do the final anneal
diffuse time=20 temp=950
struct outf=ldd.str
262
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 5: LDD Cross Section
This anneal will be carried out for 20 minutes at 950˚C. The structure is
saved in the file ldd.str. At this point, any of the structure files can be read
back and examined to check the results. Commands and analysis similar to
that found in Example 4 may be performed.
To just perform a simple check, the following commands should produce a
plot.
plot.2d bound fill y.max=1.0
select z=log10(phos+ars)-log10(bor)
contour val=0.0
The first command plots the device outline. The second command selects
the difference in the logs of the doping. This tends to produce much
smoother contours for plotting purposes. The final command plots the
junction location, as shown below.
FIGURE 1
Final LDD Device Structure.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
263
EXAMPLE 5: LDD Cross Section
To prepare a PISCES-II structure file, the following input deck, found in
“example/exam5/sup2pis.s4” can be used.
#make the contact hole
etch oxide right p1.x=1.4
#put down the aluminum and etch off
deposit alum thick=0.1
etch alum left p1.x=1.4
#remove extra grid nodes to save Pisces compute time
etch start x=-0.5 y=-0.1
etch cont x=1.6 y=-0.1
etch cont x=1.6 y=-1.0
etch done x=-0.5 y=-1.0
#reflect the structure
struct mirror left
#save it in Pisces format
struct pisc=ldd.mesh
The first line etches the oxide to form the drain contact hole. Aluminum is
deposited and etched to form contact to the drain. Everything more than
0.1µm above the surface silicon is removed. This material is uninteresting
to PISCES-II since it can not solve for anything more than the silicon substrate. The poly and oxide would just be wasted nodes. This etch uses the
polygon specification for illustration. Any number of points forming a
polygon can be specified. The material inside this polygon will be removed. The structure is reflected around the left edge. This doubles the
number of nodes and forms the complete device with both source and
drain contacts.
The structure is saved in PISCES-II format in the file ldd.mesh. This command also reports the location of contacts in the mesh for PISCES-II.
Electrode 1: xmin
ymax -0.025
Electrode 2: xmin
ymax
0.005
264
-0.550 xmax
0.550 ymin
-0.100
1.400 xmax
1.500 ymin
-0.100
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 5: LDD Cross Section
Electrode 3: xmin
ymax
0.005
Electrode 4: xmin
ymax
3.000
-1.500 xmax
-1.400 ymin
-0.100
-1.500 xmax
1.500 ymin
3.000
From this information, the gate is electrode number 1, the source and drain
are 2 and 3, and the backside contact is number 4. The file ldd.mesh can be
read by the latest release of PISCES-II and is a “geom” type file.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
265
EXAMPLE 5: LDD Cross Section
266
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 6: One Dimensional Oxide Growth
EXAMPLE 6
One Dimensional Oxide Growth
DESCRIPTION
This example compares the oxide thickness grown for different orientations. The input file for the simulation is in the “examples/exam6” directory, in the file “oxcalib.s4”.
#---some set stuff
option quiet
unset echo
foreach O (100 110 111)
echo "---------- Orientation < O > -------------------"
#---the minimal mesh
line x loc = 0.0 tag = left
line x loc = 1.0 tag = right
line y loc = 0.0 tag = top
line y loc = 1.0 tag=bottom
region silicon xlo = left xhi = right ylo = top yhi =
bottom
bound exposed xlo = left xhi = right ylo = top yhi =
top
init ori=O
#---the oxidation step
meth
grid.ox=0.03
diffuse time=30 temp=900 wet
select z=y*1e8 label="Depth(A)"; print.1d x.v=0
form=8.0f
end
The first two lines keep the program as quiet as possible. The minimum
output is printed, and the input is not echoed at all.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
267
EXAMPLE 6: One Dimensional Oxide Growth
The loop
foreach O (100 110 111) … end
runs its body three times for three different orientations.
The first seven lines of the loop body define the simplest mesh possible. It
has exactly four lines (one rectangle), and a front side.
The method command chooses the oxide grid spacing to be 0.03µm,
knowing that 30 minutes at 900˚C will grow about 0.1µm of oxide. The
oxidation step chooses the vertical model by default. The vertical model
solves the Deal-Grove diffusion equation for oxidant, and uses the calculated velocities to move the oxide vertically everywhere. For the purposes
of thickness on a planar or near-planar structure, the accuracy is good
enough. Grid is added automatically to the oxide as it grows, by default at
increments of 0.1µm. The time step is initially 0.1second; subsequently it
is automatically chosen to add no more than 14 of the grid increment per
time step.
When the diffusion is done, the select statement fills the “z vector” with
the y (vertical) locations of the points, scaled to angstroms. The print
statement then prints the y displacements along the left side of the mesh.
The form parameter rounds off the thickness to the nearest angstrom. The
output is:
"---------- Orientation < 100 > --------------------"
estimated first time step 1.286963e-16
Solving
0 +
0.1 =
0.1,
100%,np
Solving
0.1 +
302.52 =
302.62,
302520%,np
Solving
302.62 + 302.522 = 605.142, 100.001%,np
Solving 605.142 + 311.041 = 916.183, 102.816%,np
Solving 916.183 + 319.326 = 1235.51, 102.664%,np
Solving 1235.51 + 327.623 = 1563.13, 102.598%,np
Solving 1563.13 + 236.869 =
1800, 72.2992%,np
layer material
thickness Integrated
num
type
microns
Depth(A)
268
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
6
6
6
6
6
8
8
EXAMPLE 6: One Dimensional Oxide Growth
0
oxide
-0.043
0.000000e+00
1
oxide
0.000
-3.104514e-04
2
oxide
0.035
0.000000e+00
3
silicon
1.000
4.993907e-01
"---------- Orientation < 110 > --------------------"
estimated first time step 4.402759e-16
Solving
0 +
0.1 =
0.1,
100%,np 6
Solving
0.1 + 216.262 = 216.362,
216262%,np 6
Solving 216.362 + 216.266 = 432.629, 100.002%,np 6
Solving 432.629 + 224.785 = 657.413, 103.939%,np 6
Solving 657.413 +
232.98 = 890.393, 103.646%,np 6
Solving 890.393 + 241.199 = 1131.59, 103.528%,np 8
Solving 1131.59 + 249.427 = 1381.02, 103.411%,np 8
Solving 1381.02 + 257.664 = 1638.68, 103.302%,np 8
Solving 1638.68 + 161.318 =
1800, 62.6078%,np 10
layer material
thickness Integrated
num
type
microns
Depth(A)
0
oxide
-0.056
0.000000e+00
1
oxide
-0.000
-1.296132e-03
2
oxide
0.046
7.714586e-04
3
silicon
1.000
4.989346e-01
"---------- Orientation < 111 > --------------------"
estimated first time step 1.269085e-17
Solving
0 +
0.1 =
0.1,
100%,np 6
Solving
0.1 +
180.25 =
180.35,
180250%,np 6
Solving
180.35 + 180.255 = 360.605, 100.003%,np 6
Solving 360.605 + 188.773 = 549.378, 104.726%,np 6
Solving 549.378 + 196.907 = 746.285, 104.309%,np 6
Solving 746.285 + 205.073 = 951.358, 104.147%,np 8
Solving 951.358 + 213.252 = 1164.61, 103.988%,np 8
Solving 1164.61 + 221.444 = 1386.05, 103.841%,np 8
Solving 1386.05 + 229.647 =
1615.7, 103.704%,np 10
Solving
1615.7 +
184.3 =
1800, 80.2534%,np 10
layer material
thickness Integrated
num
type
microns
Depth(A)
0
oxide
-0.065
0.000000e+00
1
oxide
0.000
-1.962906e-03
2
oxide
0.053
1.281196e-03
3
silicon
1.000
4.985963e-01
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
269
EXAMPLE 6: One Dimensional Oxide Growth
The thickness is the difference between the top and bottom readings for
the oxide, namely 780Å, 1020Å and 1180Å for the <100>, <110> and
<111> orientations respectively.
270
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 7: Fully Recessed Oxide Growth
EXAMPLE 7
Fully Recessed Oxide Growth
DESCRIPTION
This example shows the evolution of an oxide profile during semi-recessed oxidation. It uses the Deal-Grove model to calculate the oxide
growth rate at the silicon/oxide interface, and treats the deformation of the
oxide and nitride as viscous incompressible flow. The input file for the
simulation is in the “examples/exam7” directory, in the file “fullrox.s4”.
#Recessed LOCOS cross section: recess 0.3um, grow
0.54um
#option quiet
#------------Substrate mesh definition
line y loc=0 spac=0.05 tag=t
line y loc=0.6 spac=0.2
line y loc=1
tag=b
line
line
line
line
x
x
x
x
loc=-1
spac=0.2 tag=l
loc=-0.2 spac=0.05
loc=0 spac=0.05
loc=1 spac=0.2 tag=r
region silicon xlo=l xhi=r ylo=t yhi=b
bound expo
xlo=l xhi=r ylo=t yhi=t
init or=100
#-----------Anisotropic silicon etch
etch
silicon left p1.x=-0.218 p1.y=0.3 p2.x=0 p2.y=0
#----------Pad oxide and nitride mask
deposit oxide thick=0.02
deposit nitride thick=0.1
etch
nitride left p1.x=0
etch
oxide
left p1.x=0
plot.2d grid bound
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
271
EXAMPLE 7: Fully Recessed Oxide Growth
#----------Field oxidation
meth compr
plot.2 bound y.mi=-0.5 line.b=2
diffuse tim=90 tem=1000 weto2 movie="plot.2 b cle=f
axi=f"
stru
outf=fc.mesh
plot.2d bound flow vleng=0.1
The first line
option quiet
asks for as little output as possible.
The grid definition comes next. First the vertical lines are defined:
line y loc=0 spac=0.05 tag=t
line y loc=0.6 spac=0.2
line y loc=1
tag=b
Ninety minutes in 1000˚C steam grows about 0.54µm of oxide on <100>
silicon. In the process, 0.24µm of silicon is consumed. The second line is
around the expected final depth of the oxide, and there is one more line at
1µm to round out the grid.
line
line
line
line
x
x
x
x
loc=-1
spac=0.2 tag=l
loc=-0.2 spac=0.05
loc=0 spac=0.05
loc=1 spac=0.2 tag=r
The x lines run from -1 to 1 for symmetry, with the mask edge at 0. The
extra refinement around 0.25µm is to prepare for the silicon etch, which
will be at an angle of 54˚ and therefore has a lateral extent of 0.3µm/
tan54˚ ≈ 0.218.
region silicon xlo=l xhi=r ylo=t yhi=b
bound expo
xlo=l xhi=r ylo=t yhi=t
init or=100
272
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 7: Fully Recessed Oxide Growth
The region statement identifies the entire area as silicon substrate. It refers
to the tags defined on the x and y lines. These tags are used to label lines
uniquely so that new lines can be added or subtracted easily without renumbering. The boundary statement identifies the top surface as being exposed. (SUPREM-IV.GS does not assume the top is exposed.) Layer
depositions, oxidations and impurity predepositions only happen on “exposed” surfaces, so this statement must not be omitted. The initialize command causes the initial rectangular mesh to be generated. The substrate
orientation is <100>.
#-----------Anisotropic silicon etch
etch
silicon left p1.x=-0.218 p1.y=0.3 p2.x=0 p2.y=0
The silicon substrate is etched. The etch statement removes all silicon
found lying to the left of the line joining the points (-0.218, 0.3) and (0,0).
#----------Pad oxide and nitride mask
deposit oxide thick=0.02
deposit nitride thick=0.1
etch
nitride left p1.x=0
etch
oxide
left p1.x=0
plot.2d grid bound
The pad oxide is put down, then nitride is deposited on top and patterned.
The patterning is presumed to remove the underlying pad oxide also. The
plot command shows the structure before oxidation and is shown in
Figure 1.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
273
EXAMPLE 7: Fully Recessed Oxide Growth
FIGURE 1
Initial grid structure before oxidation.
#----------Field oxidation
meth compr
The compressible flow model is chosen for oxidation. The incompressible
model could also have been used, but for this example where the stress is
not desired, the compressible model is faster and nearly as accurate.
plot.2d bound y.mi=-0.5 line.b=2
diffuse tim=90 tem=1000 weto2 movie="plot.2 b cle=f
axi=f"
The diffuse statement is the point of the exercise. For 90 minutes, oxide
grows at the silicon interface. The new oxide being formed pushes up the
old oxide and nitride layers which cover it, causing the characteristic bird's
head profile. The movie parameter lists any extra actions to take at each
time step. In this case, the boundary is plotted without erasing or re-scal-
274
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 7: Fully Recessed Oxide Growth
ing the picture. A series of outlines is generated, one from each time step,
illustrating the evolution of the oxide profile (Figure 2). The first plot.2d
bound defined a plotting window large enough so that the subsequent plots
without axes would fit inside it.
FIGURE 2
Evolution of bird’s head profile.
plot.2d bound flow vleng=0.1
The flow pattern at the last time step can be plotted with the statement
above. The parameter vleng is the length to draw the longest velocity vector. The other vectors are scaled proportionally. This results in Figure 3.
The flow is normal at the interface but becomes more vertically oriented
away from it.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
275
EXAMPLE 7: Fully Recessed Oxide Growth
FIGURE 3
Flow vectors at the end of oxidation.
276
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 8: Shear Stress
EXAMPLE 8
Shear Stress
DESCRIPTION
This example calculates the extent of shear stress in the silicon substrate,
generated by a film edge. It is well known that when Si3N4 is deposited on
silicon by chemical vapor deposition, a large intrinsic stress is present in
the layer. If the film is continuous and sufficiently thin, this stress does not
present a problem. The substrate is much thicker (~1000 times) than the
film, so the substrate stress is 1000 times less than the film stress. If the
film is etched, however, there is a localized stress in the silicon close to the
film edge which is of the same order of magnitude as the stress in the film.
This large stress can induce dislocations directly, or indirectly through
several mechanisms. It can also induce dislocations to glide from implanted regions into masked regions, causing junction leakage. Similar stress
patterns are set up by thermal expansion mismatches between the substrate
and overlying films.
A simulation of the substrate stress induced by a nitride film is shown below. This example can be found in the examples/exam8 directory under
the name. A <111> substrate is considered with mask edges aligned along
the <110> directions. The nitride film is 0.02µm thick. The intrinsic stress
in the nitride is assumed to be 1.4×1010 dynes/cm2, as reported in Irene
[1].The input deck for the simulation begins as follows.
#
# nitride on silicon example
foreach SEP ( 10 5 4 2.5 )
line x loc=( - SEP ) tag=l
line x loc=-2 spac=0.3
line x loc= 0 spac=0.1 tag=m
line x loc= 2 spac=0.3
line x loc= ( SEP ) tag=r
line y loc=0 spac=0.1 tag=si
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
277
EXAMPLE 8: Shear Stress
line y loc=2 spac=0.3
line y loc=5 tag=b
region silicon xlo=l xhi=r ylo=si yhi=b
bound expos
xlo=l xhi=r ylo=si yhi=si
initial ori=111
Quite a large piece of substrate is analyzed, starting with a space 10µm by
5µm. The foreach loop chooses four different widths to examine the effect of different stripe separations. The structure being simulated has reflecting boundary conditions (no perpendicular displacement) on the left
and right sides. Those boundary conditions correspond to a single instance
of a repeating pattern of nitride stripes. When the stripes are widely separated, there is little interference between the stress field of one stripe and
the next, and the results are found to be independent of the stripe separation. At smaller separations, the patterns begin to overlap. This example
will show the stress pattern for widely separated stripes and the modifications that occur as the stripes are brought closer together.
The backside of the wafer also has a reflecting boundary condition. Although that approximation is not quite physical, the nitride film primarily
exerts a horizontal force on the substrate, the assumption does not seriously affect the result. This can be verified by using different backside thicknesses; 2µm or 100µm gives identical results. The exposed surface is the
only surface with free displacements. The spacing around the film edge is
0.1µm. This could be reduced for more accuracy, at the cost of more cpu
time.
deposit nitride thick=0.02 div=2
etch
nitride left p1.x = 0
The nitride is deposited directly on silicon and patterned.
material
intrin.sig = 1.4e10 nitride
The initial nitride stress is specified in dynes/cm2.
stress
278
temp1=1000 temp2=1000
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 8: Shear Stress
This calculates the stress distribution arising from the nitride initial stress.
Stress arising from thermal expansion mismatch would be included by
specifying a different temp2. Be warned that large thermal steps often
bring into play many more complicated phenomena than the simple thermal expansion mismatch analyzed in SUPREM-IV.GS. For instance
breakdown of film adhesion or structural change may occur, but are not
taken into account in the program.
The principal slip system in silicon is in the <110> direction on 111
planes. This corresponds to the σxy shear force in the plane of the simulation. The value 3×107 is considered by Hu[2] to be the critical shear stress
for slip in silicon. Dislocations found in regions where the shear stress is
larger than that value will move under the stress field of the nitride film.
Therefore when analyzing stress in the substrate, a principal concern is the
extent of the σxy equal to 3×107 contour.
plot.2 bound x.mi=-2 x.ma=2 y.ma=4 cl=f
select z=Sxy
contour val=-3e7
The contours of σxy equal to 3×107 in the silicon are shown in Figure 1.
The contour is a double lobe because the shear stress is related to the polar
components of stress through σxy = ( σrr - σθθ) sin 2θ + σrθ cos 2θ σrr
sin 2θ. The function sin 2θ is at a maximum around 45˚ from the vertical,
and is zero at θ = 90˚. Both σrr and cos 2θ change sign moving from left to
right, so that the sign of σxy is the same throughout. This means that a dislocation which is being driven under the mask by the stress field will continue to move in that direction after passing the mask edge. However as it
passes through the center, the decrease in shear stress may leave it stranded under the mask edge. The figure shows that the area of influence of the
nitride film is many times greater than its thickness, about ±2µm horizontally, and 1.5µm vertically.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
279
EXAMPLE 8: Shear Stress
FIGURE 1
Critical Shear Stress Contours.
The largest lobe corresponds to the 10µm stripe. The result for the 5µm
stripe lies so closely on top that it cannot be distinguished. Thus either can
be a reasonable approximation for infinitely separated stripes. The 4µm
and 2.5µm lobes are somewhat smaller. This shows that the shear stress
fields from neighboring stripes tend to cancel each other in their overlap
areas, reducing the influence of the nitride film somewhat.
References
1. E. A. Irene, J. Electronic Mat., 5(3), p. 287, (1976).
2. S. M. Hu, “Film-edge-induced Stress in Silicon Substrates,” Appl.
Phys. Lett, 32(1), p. 5, 1978
280
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 9: Stress Dependent Oxidation
EXAMPLE 9
Stress Dependent Oxidation
DESCRIPTION
This example shows the use of the stress-dependent oxidation model. Experimental LOCOS profiles are generally of two distinct types [1]. When
the nitride mask is more than two to three times thicker than the pad oxide,
the oxide/silicon interface and the oxide gas surface is kinked. For thinner
nitride masks, the shape can be approximately be described by an errorfunction. The kinks were not observed in the first generation of oxidation
simulators, because they result from stress effects on the growth coefficients. Early oxidation programs did not take stress into account and found
essentially identical oxide shapes irrespective of nitride thickness. This example shows how the stress-dependent model in SUPREM-IV.GS can predict such second-order effects. The example is given in the file “sdep.s4”
in the “examples/exam9” directory.
The grid structure and nitride/oxide sandwich is very similar to the fullyrecessed oxide example. The substrate grid is as sparse as possible (two
lines). The lateral grid is a little coarse to compensate for the increased
computation time used in the nonlinear model.
The new statements are as follows:
oxide stress.dep=t
The nonlinear stress-dependent model is turned on. The default is to turn it
off since it is much more expensive to run than the linear model.
The activation volume for plastic flow Vc, for the stress-dependent reaction rate Vr, and for the diffusivity Vd, are taken from the defaults in the
model file. The values used were derived by fitting Kao’s cylinder oxidation data [2].
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
281
EXAMPLE 9: Stress Dependent Oxidation
meth
viscous oxide.rel=1e-2
The viscous model is chosen, because only this model takes stress effects
into account. (Only the viscous model calculates stress accurately enough
to feed back into the coefficients). The relative error criterion is chosen as
1% in the velocities. The default of 10-6 is rather tight and requires more
CPU time.
The diffuse statement is as usual.
This input file was executed twice, once with 0.05µm of nitride and once
with 0.15µm of nitride. The output contains the usual features, along with
many lines as follows:
Newton loop 0 cut 1
upd
0.9914 o r h s
3.811
rhs 3.534e-15
Newton loop 1* cut 1
upd 1.322e-12 orhs 3.534e-15
rhs
1e-38
Continuation step #0 to lambda = 0.25 step 0.25
Newton loop 0 cut 1
upd 0.008394 orhs 0.0002229
rhs 0.0003045
Newton loop 0 cut 0.25 upd 0.008394 orhs 0.0002229
rhs
0.000135
Newton loop 2 cut 0.25 upd 0.005944 orhs 0.0001278
rhs
6.63e-05
Newton loop 4 cut 0.5 upd 0.004301 orhs 6.479e-05
rhs 1.638e-05
Newton loop 5* cut
1 upd 0.002137 orhs 1.638e-05
rhs
1.43e-05
Newton loop 7 cut
1 upd 0.000463 orhs 1.625e-05
rhs
1e-38
Continuation step #0 to lambda = 0.5 step 0.25
Newton loop 0 cut
1 upd
0.1527 orhs
0.0359
rhs
0.04011
...
Newton loop 4 cut 0.031 upd
2.062 orhs
0.01961
rhs
0.0199
Continued too far, backing off.
Continuation step #-1 to lambda = 0.375 step 0.125
Newton loop 0 cut
1 upd
0.06759 orhs
0.02686
rhs
0.02223
282
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 9: Stress Dependent Oxidation
Newton loop 2 cut
1 upd
0.1005 orhs
0.02204
rhs
0.02313
&...
Newton loop28 cut 0.5 upd
0.00263 orhs 0.0005139
rhs 0.0002645
Newton loop30 cut
1 upd 0.0009523 orhs 0.0002647
rhs
1e-38
Continuation step #0 to lambda = 0.5 step 0.125
Newton loop 0 cut
1 upd
0.01423 orhs
0.01075
rhs
0.008121
Newton loop 2 cut
1 upd 0.002104 orhs
0.008299
rhs
0.003507
Newton loop 4 cut
1 upd 0.002404 orhs
0.003543
rhs
0.007114
Newton loop 4 cut 0.25 upd 0.002404 orhs
0.003543
rhs
0.002892
Newton loop 6 cut 0.25 upd 0.0007027 orhs
0.002888
rhs
1e-38
Continuation step #0 to lambda = 1 step 0.5
Newton loop 0 cut
1 upd 0.0005178 orhs
0.002156
rhs
1e-38
The nonlinear solver works by proceeding first from the linear solution.
The linear solution takes exactly two Newton steps. The first has a large
update step 0.9914, which reduces the error from 3.811 to 3.5e-15. The
second Newton step 1.3e-12 then of course is trivial since the solution has
been reached. The Newton loop counter is incremented by two whenever a
new Jacobian is factorized, and by one when only the error is recalculated.
The stress-dependent viscosity is turned on (continuation step 0 to lambda
= 0.25). The first step is moderately large 0.008394 and causes the error to
increase 0.00022 to 0.0003045. A quarter-step (cut 0.25) in that direction
is tried, which is found to decrease the error from 0.00022 to 0.0001. This
new position is accepted as worthwhile, and a second Newton step is taken
from there. It is found to decrease the error from 0.0059 to 0.00012. Since
this is successful, the cutback factor is increased back to 0.5.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
283
EXAMPLE 9: Stress Dependent Oxidation
The third Newton step (#4) reduces the error by a large factor, so on the
subsequent step not only is the length increased back to 1 but the same Jacobian is recycled, indicated by the asterisk. The recycled Jacobian proves
not to be effective, since the error only goes from 1.6e-5 to 1.4e-5. One
more Jacobian is factored, and causes an update of 0.0004636, less than
the accuracy criterion. The first nonlinear problem has been solved.
The stress-dependent reaction rate is then turned on (continuation to 0.5).
In this case, the Newton process fails. Successively smaller steps along the
Newton direction are taken, but at each attempted new position the error is
larger than the current location. The smallest step tried is 0.031; the next
would be 0.031/4 which is less than 1% of the Newton update and the situation is considered hopeless. The program then backs off by trying an intermediate lambda of 0.375. This corresponds to a stress dependence
which is only half as strong as the desired dependence. After 15 Newton
steps, this weaker problem is solved. The solution is then used as an initial
guess for the problem first tried, that with the full stress dependence
(lambda = 0.5). The improved initial guess leads to a successful solution
of the problem after 3 Newton steps. Finally, the stress-dependent diffusivity is turned on (lambda =1). Since the activation volume for diffusivity
was left at 0, nothing of interest happens and the problem is solved after
one loop. The total number of Newton loops is therefore about 24, compared to 1 for a linear problem. Thus the nonlinear problem is about 24
times as expensive to solve as a linear problem.
The different oxide shapes are shown in Figures 1 and 2. The thicker nitride clearly has the effect of reducing the bird's beak.
284
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 9: Stress Dependent Oxidation
FIGURE 1
Comparison of LOCOS Shapes with 500Å Nitride and 1500Å Nitride.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
285
EXAMPLE 9: Stress Dependent Oxidation
FIGURE 2
Comparison of LOCOS Shapes with 500Å Nitride and 1500Å Nitride.
References
1. 1. N. Guillemot, G. Pananakakis and P. Chenevier, IEEE Transactions
on Electron Devices, ED-34, (1987).
2. 2. D.-B. Kao, J. P. McVittie, W. D. Nix and K. C. Saraswat, “Two-Dimensional Silicon Oxidation Experiments and Theory,” IEDM Tech.
Digest, 1985,
286
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 10: GaAs MESFET Gate Simulation – 1D
EXAMPLE 10
GaAs MESFET Gate Simulation – 1D
DESCRIPTION
This example simulates a simple 1D GaAs MESFET structure underneath
the gate. This utilizes SUPREM-IV.GS's new true 1D mode. First, the 1D
grid is set up and initialized with carbon as a background dopant. Beryllium and silicon are implanted into GaAs. Note that silicon as an impurity is
designated as “isilicon”. The as-implanted dopant concentration-depth
profiles are plotted in 1D in Figure 1. Next an anneal step is done, using
the Fermi method, and the diffused beryllium profile is then plotted in the
same figure. The hump in the beryllium profile at the beryllium/silicon
junction is due to the electric field effect on diffusion. Since the beryllium
was implanted, the implanted diffusivity numbers (as opposed to the
grown-in numbers) are used. The input file for the simulation is in the
“examples/exam10” directory, in the file example10.in.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init carbon conc=1e15
implant beryllium dose=2e13 energy=100 pearson
implant isilicon dose=5e13 energy=50 pearson
#beryllium gaas Dip.0=2.1e-8 Dip.E=1.74
beryllium gaas /nitride Seg.0=.5 Seg.E=0
deposit nitride thick=.3
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
287
EXAMPLE 10: GaAs MESFET Gate Simulation – 1D
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20
line.type=2
select z=log10(isilicon)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=3
select z=log10(carbon)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=4
method fermi init=1e-5
method full.fac
diffuse time=15 temp=800 argon
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=5
quit
If you wish to change the beryllium diffusivity parameters, you would uncomment the line:
#beryllium gaas Dip.0=2.1e-8 Dip.E=1.74
and put in your own values.
288
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 10: GaAs MESFET Gate Simulation – 1D
FIGURE 1
Beryllium, Silicon, and Carbon profiles under the MESFET gate.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
289
EXAMPLE 10: GaAs MESFET Gate Simulation – 1D
290
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 11: GaAs Simulation – 2D
EXAMPLE 11
GaAs Simulation – 2D
This shows how one would do a 2D GaAs simulation. A 2D grid is set up,
and silicon and beryllium are implanted in the source, drain and channel
regions. Then the doping contours are plotted for the designated concentration levels in Figure 2. In this example, only one half of the structure is
simulated, then mirrored before the result is plotted, in order to speed up
simulation time. The input file for the simulation is in the “examples/
exam11” directory, in the file example11.in.
option quiet
set echo
line
line
line
line
line
line
line
x
x
x
x
x
x
x
loc
loc
loc
loc
loc
loc
loc
=
=
=
=
=
=
=
0.0 tag=left
0.50
4.00
4.10
4.20
4.50
5.00 tag=right
spacing
spacing
spacing
spacing
spacing
spacing
spacing
=
=
=
=
=
=
=
0.5
0.5
0.5
0.1
0.05
0.05
0.05
line
line
line
line
y
y
y
y
loc=0.0 tag=top
spacing=0.03
loc=0.3
spacing=0.03
loc=1.0
spacing=0.1
loc=3.0 tag=bottom spacing=0.3
region gaas xlo=left xhi=right ylo=top yhi=bottom
boundary exposed xlo=left xhi=right ylo=top yhi=top
boundary backside xlo=left xhi=right ylo=bottom yhi=bottom
init isilicon conc=3e15
deposit nitride thick=1.0
etch nitride start x=5 y=0.0
etch continue x=5 y=-1.10
etch continue x=4.5 y=-1.10
etch done x=4.5 y=0.0
implant isilicon dose=1.75e12 energy=75 pearson
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
291
EXAMPLE 11: GaAs Simulation – 2D
implant beryllium dose=1e13 energy=100 pearson
etch
etch
etch
etch
nitride start x=4.5 y=0.0
continue x=4.5 y=-1.10
continue x=0 y=-1.10
done x=0 y=0.0
deposit nitride thick=1.0
etch nitride start x=4.5 y=0.0
etch continue x=4.5 y=-1.10
etch continue x=0.0 y=-1.10
etch done x=0.0 y=0.0
implant isilicon dose=1e13 energy=100.0 pearson
etch
etch
etch
etch
nitride start x=4.5 y=0.0
continue x=4.5 y=-1.10
continue x=5.0 y=-1.10
done x=5.0 y=0.0
deposit nitride thick=.05
structure mirror right
plot.2d bound fill x.min=4.0 x.max=6 y.max=1.6
select z=log10(isilicon)
foreach v (15. to 18.5 step 0.5)
contour val=v line.type=2
end
plot.2d bound fill x.min=4 x.max=6 y.max=1.6 cle=f
axi=f
select z=log10(beryllium)
foreach v (16.5 to 17.0 step .5)
contour val=v line.type=4
end
quit
292
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 11: GaAs Simulation – 2D
FIGURE 1
Beryllium and Silicon contours in the MESFET source, drain, and channel
regions.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
293
EXAMPLE 11: GaAs Simulation – 2D
294
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 12: Dopant Activation Model Example
EXAMPLE 12
Dopant Activation Model Example
Here the SUPREM-IV.GS dopant activation model is illustrated. The input
file for the simulation is in the “examples/exam12” directory, in the file example12.in.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.02 tag=top
x loc=0.5 spacing=0.02
x loc=20 spacing=0.25 tag=bottom
region gaasxlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init beryllium conc=3e17
implant isilicon dose=5e13 energy=100 pearson
#material gaas
act.b="1.00e21"
#material gaas
act.b="4.25e18"
p.type
act.a="(2.2 - 0.00117 * T)"
n.type
act.a="(2.2 - 0.00117 * T)"
deposit nitride thick=.3
method fermi init=1e-5
diffuse time=.001 temp=750 argon
select z=log10(isilicon)
plot.1d x.mi=0 x.ma=2 y.mi=14 y.ma=20 line.type=1
select z=log10(electrons)
plot.1d x.mi=0 x.ma=2 y.mi=14 y.ma=20 cle=f axi=f
line.type=2
select z=log10(abs(doping))
plot.1d x.mi=0 x.ma=2 y.mi=14 y.ma=20 cle=f axi=f
line.type=3
quit
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
295
EXAMPLE 12: Dopant Activation Model Example
Silicon is implanted into GaAs with a beryllium doped background.
Figure 1 shows the 1D plot of this. The default n and p-type activation
models are used, commented out in the lines:
#material gaas p.type act.a="(2.2 - 0.00117 * T)"
act.b="1.00e21"
#material gaas n.type act.a="(2.2 - 0.00117 * T)"
act.b="4.25e18"
Plotted in Figure 1 are the silicon profile, the electron profile, and the net
doping profile. The electron profile takes into account the less than 100
percent net n-type dopant activation under the silicon peak, as well as the
reduced electron concentration in the bulk due to the beryllium background doping. The abs(doping) profile clearly shows the silicon/beryllium n/p junction.
Figure 2 shows the results when the n-type activation model parameters
are changed. In this case, the following line is included:
material gaas n.type act.a="(2.2 - 0.00117 * T)"
act.b="4.25e18"
Note that the act.b parameter has been changed. This increases the net active n-type dopant concentration under the peak of the silicon implant profile.
296
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 12: Dopant Activation Model Example
FIGURE 1
Silicon, electrons, and net doping profiles for a silicon/beryllium MESFET
structure. The default activation models are used for silicon.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
297
EXAMPLE 12: Dopant Activation Model Example
FIGURE 2
Same as Figure 1 except that modified silicon activation numbers are used,
resulting in a higher silicon activation.
298
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 13: Implanted and Annealed Beryllium
EXAMPLE 13
Implanted and Annealed Beryllium
Examples 13, 14, and 15 illustrate the differences in using implanted vs.
grown-in dopants, and how it effects the diffusivity values used. In
Example 13, beryllium is implanted in GaAs, and the structure is annealed. The input file for the simulation is in the “examples/exam13” directory, in the file example13.in. The as-implanted and diffused beryllium
profiles are shown in Figure 1. The implanted diffusion coefficients are
used since there is an “implant beryllium ...” statement.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init carbon conc=1e15
implant beryllium dose=1e14 energy=100 pearson
deposit nitride thick=.3
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20
line.type=4
method fermi init=1e-5
method full.fac
diffuse time=15 temp=800 argon
select z=log10(beryllium)
plot.1d x.mi=0 x.ma=2 y.mi=14 y.ma=20 cle=f axi=f
line.typ=2
quit
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
299
EXAMPLE 13: Implanted and Annealed Beryllium
FIGURE 1
Implanted and annealed beryllium using the implanted diffusion
coefficients.
300
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 14: Grown-in and Annealed Beryllium
EXAMPLE 14
Grown-in and Annealed Beryllium
The input file for this simulation is in the “examples/exam14” directory, in
the file example14.in.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init beryllium conc=1e15
deposit gaas thick=.5 divisions=100 beryllium
conc=5e18
deposit gaas thick=.5 divisions=100 beryllium
conc=1e15
deposit nitride thick=.3
select z=log10(beryllium)
plot.1d x.min=-1 x.ma=1 y.mi=14 y.max=20
line.type=4
method fermi init=1e-5
method full.fac
diffuse time=15 temp=800 argon
select z=log10(beryllium)
plot.1d x.min=-1 x.ma=1 y.mi=14 y.max=20 cle=f
axi=f line.type=2
quit
Here, Be is grown into the GaAs by using the deposit statements
deposit gaas thick=.5 divisions=100 beryllium
conc=5e18
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
301
EXAMPLE 14: Grown-in and Annealed Beryllium
deposit gaas thick=.5 divisions=100 beryllium
conc=1e15
instead of an implant statement. In this case, SUPREM-IV.GS uses the
lower “as-grown” diffusivities for beryllium since no implanted beryllium
is present. The as-grown and diffused profiles are shown in Figure 5. The
extent of beryllium diffusion is seen to be much less in this case compared
to the implanted case (Example 13), even though the same anneal conditions are used and the beryllium peak concentrations are comparable (the
diffusion is hole, or concentration, dependent).
FIGURE 1
Grown-in and annealed beryllium in GaAs using the grown-in diffusion
coefficients.
302
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 15: Annealing An Implant From Measured (SIMS) Data
EXAMPLE 15
Annealing An Implant From Measured (SIMS)
Data
In this example, the “implanted” diffusivities are used, even though there
is no implant statement. The input file for the simulation is in the “examples/exam15” directory, in the file example15.in.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init carbon conc=1e15
profile infile=be1 beryllium
implant beryllium dose=1e1 energy=100 pearson
deposit nitride thick=.3
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20
line.type=4
method fermi init=1e-5
method full.fac
diffuse time=15 temp=800 argon
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=2
quit
The as-implanted profile obtained from SIMS measurements is input from
a file (“be1”) by using the profile statement:
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
303
EXAMPLE 15: Annealing An Implant From Measured (SIMS) Data
profile infile=be1 beryllium
File be1 contains the x concentration values for the as-implanted beryllium profile. In order to use the “implanted” diffusivities even though there
is no implant statement a “dummy” implant is done,
implant beryllium dose=1e1 energy=100 pearson
in which a very low dose beryllium implant is used. As shown in Figure 1,
the extent of diffusion is comparable to that of Example 13, and much
more than in Example 14, indicating the higher “implanted” diffusivity is
used.
FIGURE 1
Implanted beryllium from SIMS data and SUPREM-IV.GS annealed profile.
304
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 16: Two.Dim Diffusion With File Input Interstitials
EXAMPLE 16
Two.Dim Diffusion With File Input Interstitials
Here the two.dim method for diffusion is illustrated. The input file for the
simulation is in the “examples/exam16” directory, in the file example16.in.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init carbon conc=1e15
implant beryllium dose=1e14 energy=100 pearson
profile infile=file1 inter
deposit nitride thick=.3
interstitial gaas
interstitial gaas
interstitial gaas
interstitial gaas
0.
interstitial gaas
pos.E=0 dneg.0=0
interstitial gaas
tneg.0=0
D.0=5e-14
D.E= 0.
Kr.0=1e-18
Kr.E= 0.
Cstar.0= 1.0e16
Cstar.E= 0.
/nitride Ksurf.0= 1e-3
Ksurf.E=
neu.0=0 pos.0=1 neu.E=0 neg.0=0
dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0
vacancy gaas D.0= 1e-15
D.E= 0.
vacancy gaas Kr.0=1e-18
Kr.E= 0.
vacancy gaas Cstar.0= 1e16
Cstar.E= 0.
vacancy gaas /nitride Ksurf.0= 1e-3
Ksurf.E= 0.
vacancy gaas neu.0=0 pos.0=0 neu.E=0 neg.0=0 pos.E=0
dneg.0=0
vacancy dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0 tneg.0=1
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
305
EXAMPLE 16: Two.Dim Diffusion With File Input Interstitials
method full.fac
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20
line.type=4
select z=log10(inter)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=2
method two.dim init=1e-5
diffuse time=15 temp=800 argon
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=4
select z=log10(inter)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=2
quit
In Example 13, the Fermi method for diffusion was used, in which it is assumed that interstitial and vacancy concentrations are at their equilibrium
values throughout the simulation. Therefore, the diffusivities are only dependent on temperature and the local doping concentrations (n or p). In
Example 14, the two.dim method for diffusion is used, in which extrinsic
interstitials or vacancies (i.e. added from some source, such as implant
damage, or from oxidation in the case of silicon technology) are taken into
account in the diffusion of dopants. In this case I/I* or V/V* may not equal
one, and these terms are included in the diffusion equations. In this example, the interstitial profile is input by the statement:
profile infile=file1 inter
where file1 contains the x concentration values for the interstitials that
might be caused by implantation damage. Now the statement:
method two.dim init=1e-5
306
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 16: Two.Dim Diffusion With File Input Interstitials
is used, rather than the fermi method statement. Parameters for various interstitial and vacancy properties are also included. For example, only +1
charge state interstitials are used, according to the statements:
interstitial gaas neu.0=0 pos.0=1 neu.E=0 neg.0=0
pos.E=0 dneg.0=0
interstitial gaas dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0
tneg.0=0
The as-implanted and diffused profiles of beryllium and interstitials are
shown in Figure 1. The diffused beryllium profile is much different than
that in Example 13, where the fermi method was used (with no added interstitials). The simulation predicts the famous “uphill diffusion” of implanted p-type dopants often observed.
FIGURE 1
Beryllium and interstitial profiles, before and after anneal, using the two.dim
method for diffusion. The excess interstitials (above I*) produce “uphill
diffusion” of Beryllium.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
307
EXAMPLE 16: Two.Dim Diffusion With File Input Interstitials
308
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 17: Full.Coupled Diffusion
EXAMPLE 17
Full.Coupled Diffusion
The input file for the simulation is in the “examples/exam17” directory, in
the file example17.in. In this example, the full.coupled method of diffusion is illustrated.
option quiet
set echo
mode
line
line
line
one.dim
x loc=0.0 spacing=0.01 tag=top
x loc=1.0 spacing=0.01
x loc=20 spacing=0.25 tag=bottom
region gaas
xlo=top xhi=bottom
boundary exposed xlo=top xhi=top
boundary backside xlo=bottom xhi=bottom
init carbon conc=1e15
implant beryllium dose=1e14 energy=100 pearson
deposit nitride thick=.3
interstitial gaas
interstitial gaas
interstitial gaas
interstitial gaas
interstitial gaas
pos.E=0 dneg.0=0
interstitial gaas
tneg.0=0
interstitial gaas
dneg.0=0 dpos.0=0
interstitial gaas
vacancy gaas
vacancy gaas
vacancy gaas
vacancy gaas
vacancy gaas
dneg.0=0
D.0=5e-14
D.E= 0.
Kr.0=1e-18
Kr.E= 0.
Cstar.0= 1.0e16 Cstar.E= 0.
/nitride Ksurf.0= 1e-3 Ksurf.E= 0.
neu.0=0 pos.0=1 neu.E=0 neg.0=0
dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0
beryllium neu.0=0 pos.0=0 neg.0=0
beryllium tneg.0=0 tpos.0=0
D.0= 1e-15
D.E= 0.
Kr.0=1e-18
Kr.E= 0.
Cstar.0= 1e16
Cstar.E= 0.
/nitride Ksurf.0= 1e-3 Ksurf.E= 0.
neu.0=0 pos.0=0 neu.E=0 neg.0=0 pos.E=0
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
309
EXAMPLE 17: Full.Coupled Diffusion
vacancy dpos.0=0 dpos.E=0 neg.E=0 tpos.0=0 tneg.0=1
vacancy gaas beryllium neu.0=0 pos.0=0 neg.0=0
dneg.0=0 dpos.0=0
vacancy gaas beryllium tneg.0=0 tpos.0=0
method full.fac
diffuse time=.00001 temp=800 argon
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20
line.type=4
select z=log10(inter)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=2
method full.cpl init=1e-5
diffuse time=15 temp=800 continue argon
select z=log10(beryllium)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=4
select z=log10(inter)
plot.1d x.min=0 x.ma=2 y.mi=14 y.max=20 cle=f
axi=f line.type=2
quit
Here Example 13 is repeated, but using the full.coupled diffusion method
rather than the fermi method. In this method, non-equilibrium levels of interstitials or vacancies can be produced by the diffusion process itself,
without adding non-equilibrium levels of defects at the beginning, as was
done in Example 16. This is because in the diffusion process, the dopant
diffuses as a dopant/defect pair, and defects are carried along with the
dopant. This can result in local regions of non-equilibrium concentrations
of defects and can in turn effect the dopant diffusion. (If one believes that
the “kick-out” mechanism is occurring rather than the pair mechanism, the
same effect occurs as the interstitial dopant kicks-out a matrix atom, creating an interstitial.) The method statement is now:
method full.cpl init=1e-5
Note that there is an initial very short diffuse statement:
310
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
EXAMPLE 17: Full.Coupled Diffusion
diffuse time=.00001 temp=800 argon
In this first diffusion step, a short time anneal is done to establish the equilibrium defect concentrations in case you want to plot the initial values of
these (since they are temperature dependent). In the second diffuse statement:
diffuse time=15 temp=800 continue argon
the continue parameter is used to maintain the initial defect values. Therefore, the initial diffuse uses the fermi method, and the defect levels are initially set at their equilibrium values. (Since the interstitials are set at the +1
charge state, the equilibrium interstitial concentration is fermi level dependent and therefore the initial interstitial profile follows the beryllium profile). The main diffusion step uses the full.cpl method. The dopant/defect
pairing parameters are specified by the following statements.
interstitial gaas beryllium neu.0=0 pos.0=0 neg.0=0
dneg.0=0 dpos.0=0
interstitial gaas beryllium tneg.0=0 tpos.0=0
These are all normally set to 0 if one assumes that the pair concentration is
much less than the defect concentration (non-equilibrium levels of defects
will still occur, since the defect flux equation in the full-coupled mode still
takes into account the extra defects produced by the diffusion process). In
Figure 1, the as-implanted and diffused beryllium and interstitial profiles
generated are shown. One can see that, compared to Example 13, a kink in
the profile occurs due to this defect non-equilibrium effect. If one increases the interstitial diffusivity in the statement:
interstitial gaas D.0=5e-14 D.E= 0.
from 5×10-14 to 1×10-11 for example, the interstitials are able to diffuse
back to their equilibrium levels everywhere, and normal “Example 13
type” diffusion occurs.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs
311
EXAMPLE 17: Full.Coupled Diffusion
FIGURE 1
Beryllium and interstitial profiles, before and after anneal, using the
full.coupled method for diffusion. Excess interstitials created by the pair (or
kickout) diffusion mechanism, result in a kink or knee in the beryllium
profile.
312
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs